some bibliography: P

[A] [B] [C] [D] [E] [F] [G] [H] [I] [J] [K] [L] [M] [N] [O] [P] [Q] [R] [S] [T] [U] [V] [W] [X] [Y] [Z] [NOAUTHORS]

Paal, Eugen

Operadic deformations as a tool for cogravity
arXiv:math.QA/0202017, 6 pages
Abstract: The deformation equation and its integrability condition (Bianchi identity) of a non-(co)associative deformation in operad algebra are found.

Operads and deformations
AGG 22 (2005), N2

Pace, Luigi and Salvan, Alessandra

The geometric structure of the expected/observed likelihood expansions
DOI: 10.1007/BF00773474
Ann. Inst. Stat. Math. 46 (1994), N4, 649-666

Pacholski, Leszek

In Memoriam: Jerzy Los, 1920-1998
The Bulletin of Symbolic Logic, Vol. 6, No. 1 (Mar., 2000), pp. 97-100

Pachter, Lior and Sturmfels, Bernd

The mathematics of phylogenomics
DOI: 10.1137/050632634
arXiv:math.ST/0409132
SIAM Review Volume 49 Issue 1 Pages 3-31, 2007
Availability: hardcopy

Padmanabhan, R and Rudeanu, S

AXIOMS FOR LATTICES AND BOOLEAN ALGEBRAS
World Sci., 2008
Description: Prover9 is utilized.

Page, Stanley S.

A characterization of rigid algebras
DOI: 10.1112/jlms/s2-2.2.237
J. London Math. Soc. 2 (1970), 237-240
Description: Of associative algebras. Over algebraically closed field, A is rigid iff H^2(A,A) = 0?
Availability: 237.pdf

Page, S. and Richardson, R.W.

Stable subalgebras of Lie algebras and associative algebras
DOI: 10.2307/1994649
Trans. Amer. Math. Soc. 127 (1967), 302-312
Zentralblatt: 0163.03003
Description: Any subalgebra h of a reductive Lie algebra g, containing a space close to a given semisimple Lie algebra s in g, contains a subalgebra, close to s (and conjugate to s).
Availability: 0-150.pdf

Pagon, Dushan

Deformations of graded nilpotent Lie algebras
Mosc. Univ. Math. Bull. 36 (1981), No.4, 62-66
Zentralblatt: 0484.17008, 0472.17004
Availability: hardcopy

Graded deformations of almost free Lie algebras
Mosc. Univ. Math. Bull. 37 (1982), No.5, 83-87 (English)
Vestn. Mosk. Univ., Ser. I 1982 (1982), No.5, 66-70 (Russian)
MR 84e:17016
Zentralblatt: 0513.17004
Description: "Almost free" means with one second order relation.

Bases and deformations of some Lie algebras (in Russian)
Proceedings of the Conference "Algebra and Logic", Cetinje 1986, 131-138, Univ. Novi Sad, Novi Sad, 1987
MR 89m:17047
Zentralblatt: 0643.17008

On contractions of Lie algebras
Algebra and logic, Proc. Conf., Sarajevo/Yugosl. 1987, 97-101 (1989)
Zentralblatt: 0729.17002
Description: Contractions of free nilpotent Lie algebras.

On cohomologies of coinduced modules of modular Lie algebras
Znan. rev., Naravosl. mat., 1990, let. 2, st. 1, 103-109

Paige, Lowell L.

A theorem on commutative power associative loop algebras
PAMS 6(1955), N2, 279-280
Description: A criterion for loop algebra to be commutative power associative.
Availability: Paige.pdf

Pakhomov, Valerii F.

Automorphisms of the tensor product of abelian and Grassmanian algebras
Math. Notes 16(1974), 624-629
Mat. Zametki 16(1974), 65-75
MR 50#9981
Availability: q148437p33496546.pdf

The story of superdeterminants
Description: An historical account of an episode from linear superalgebra

Pal, Tanusree

Almost Compact Real Forms of Twisted Affine Kac-Moody Algebras and the e-Vogan Diagrams
arXiv:0802.0665

Palamodov, V.P.

Deformations of complex spaces
Russ. Math. Surv. 31 (1976), N3, 129-197
Availability: hardcopy

Pall, Gordon

On sums of squares
Amer. Math. Monthly 40 (1933), No.1, 10-18
Availability: 1.pdf

Palmkvist, Jakob

A realization of the Lie algebra associated to a Kantor triple system
arXiv:math.RA/0504544
J. Math. Phys. 47 (2006), 023505
Description: A unified KKT-like realization of F_4 and E_6-E_8 (probably reformulation of what was known before).

Generalized conformal realizations of Kac-Moody algebras
arXiv:0711.0441
Description: Generalized KKT-like construction.

Panaite, Florin and Stefan, Dragos

Deformation cohomology for Yetter-Drinfeld modules and Hopf (bi)modules
Comm. Algebra 30(2002), N1, 331-345

Panaite, Florin and Van Oystaeyen, Freddy

Quasi-Hopf algebras and representations of octonions and other quasialgebras
Journal of Mathematical Physics -- October 2004 -- Volume 45, Issue 10, pp. 3912-3929
Description: Category of modules over the octonions is isomorphic to the category of modules over the algebra of 8x8 real matrices, as a consequence of some modules over quasi-Hopf algebras considerations.

Panasyuk, Andriy

Algebraic Nijenhuis operators and Kronecker Poisson pencils
arXiv:math.DG/0504337
Description: Nijenhuis operator on a Lie algebra L is N: L x L -> L such that [Nx,Ny] - N([Nx,y] + [x,Ny]) + N^2[x,y] = 0. Related constructions and results. Related with Lie multiplication of the form xay - yax in an associative algebra.

Pankratyev, E.V.

Computernaya algebra. Faktorizaciya mnogochlenov
Moscow Univ., 1988 (in Russian)
Availability: comput-alg.{pdf,djvu}

Panyukov, V.V.

Irreducible representations of completely solvable Lie algebras of positive characteristic
DOI: 10.1070/IM1989v032n03ABEH000783
Math. USSR Izv. 32 (1989), No.3, 607-626
MR 954299
Zentralblatt: 0654.17011

On the solvability of Lie algebras of positive characteristic
Russ. Math. Surv. 45 (1990), No.4, 181-182
Zentralblatt: 0719.17007
Availability: hardcopy

On solvable Lie algebras decomposable into a sum of two nilpotent subalgebras
Sbornik Math. 83 (1995), No.1, 221-235
Zentralblatt: 0849.17018
Abstract: This class of (solvable) algebras is further studied.
Availability: pan18510.ps

Panyushev, Dmitry I.

O neprivodimosti kommutatornykh mnogoobrazii svyazannykh s involyuciyami prostykh algebr Lie
Description: Varieties (in alg. geom. sense) of commuting elements in classical Lie algebras.
Availability: irr-com.ps

Abelian ideals of a Borel subalgebra and long positive roots
IMRN 35 (2003)

On reachable elements and the boundary of nilpotent orbits in simple Lie algebras
DOI: 10.1016/j.bulsci.2004.08.001
Bull. Sci. Math. 128 (2004), N10, 859-870
Description: An element is called reachable, if it is contained in a commutant of its centralizer (it is necessary nilpotent).

Semi-direct products of Lie algebras and their invariants
Publ. RIMS 43 (2007), 1199-1257
arXiv:math.AG/0506579

Periodic automorphisms of Takiff algebras, contractions, and \theta-groups
arXiv:0710.2113
Description: Contraction of Lie algebras g\otimes K[T]/(T^m).

Papadopoulo, Georges

On the Leibniz homology of Poisson algebras
DOI: 10.1023/A:1011072629566
Lett. Math. Phys. 54 (2000), no. 4, 237-247

Papi, Paolo

Cohomology of tensor product quantum planes
Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 3 (1992), No.1, 5-13
Zentralblatt: 0776.17020
Description: Second cohomology with trivial coefficients of Lie algebra of inner derivations of the n-fold tensor product of Manin quantum planes.

Paramonova, I.M. and Sheinman, O.K.

Zadachi seminara "Algebry Lie" i ikh prilozheniya
MCCME, 2004 (in Russian)
Availability: MCCME web site

Pareigis, Bodo

Cohomologie de p-algebres de Lie
CRAS 263 (1966), 709-712
Zentralblatt: 0168.28402
Description: A variant of restricted cohomology coinciding for n>3 with Hochschild one, and providing for n=2,3 structural interpretation (extension, kernels).
Availability: hardcopy

Kohomologie von p-Lie-Algebren
Math. Z. 104, 281-336 (1968)
Zentralblatt: 0162.33701

Forms of Hopf algebras and Galois theory
Topics in Algebra. Banach Center Publ. 26 (1990), 75-93
Description: Interesting reasoning about forms of algebraic structures in general.
Availability: somewhere on the web (file Form_Gal.ps) (?)

Parfenov, V.A.

A certain property of ideals of a free Lie algebra
Sib. Mat. Zh. 10 (1969), N10, 940-944
Sib. Math. J. 10 (1969), 690-693
Zentralblatt: 0175.31103
Description: Let V(A) be a hull of all (Lie) words in V with values on a set A. Then, over p=0, if V(A) in V(B), then A in B.

Exterior differentiations of Lie algebras
DOI: 10.1007/BF00969294
Sibirsk. Mat. Z. 17 (1976), no. 1, 113--118
Siberian Math. J. 17 (1976), no. 1, 91--95
MR 53#5684
Description: An algebra over the field p=0 generated by $A=\{a_\alpha|\alpha\in I\}$ is relatively free with free set $A$ if and only if every mapping $A\rightarrow\germ A$ can be induced by a differentiation of the algebra.

An example of a locally nilpotent Lie algebra
Mat. Zametki 26 (1979), 667-672
Description: Lie algebra [e_i,e_j]=e_{i+j} for i,j rational between 0 and 1.

Parimala, R. and Sridharan, R. and Thakur, Maneesh L.

A classification theorem for Albert algebras
Trans. Amer. Math. Soc. 350 (1998), 1277-1284
Description: Simple algebras of degree 3 with involution of the second kind, Jordan algebras, first Galois cohomology, ...

Parker, Alison E.

On the good filtration dimension of Weyl modules for a linear algebraic group
arXiv:math.RT/0507552
J. Reine Angew. Math. 562 (2003), 5-21
Description: Ext's between some (classical) modules.

Higher extensions between modules for SL_2
DOI: 10.1016/j.aim.2006.05.015
arXiv:math.RT/0508155
Adv. Math. 209 (2007), N1, 381-405

Parker, Darren B.

Forms of coalgebras and Hopf algebras
J. Algebra 239(2001), no. 1, 1-34

Parshall, Karen Hunger

Joseph H. M. Wedderburn and the structure theory of algebras
DOI: 10.1007/BF00348450
Archive for History of Exact Sciences Volume 32, Numbers 3-4 / September, 1985 Pages 223-349
Availability: 1985-joseph.pdf

Parshall, Brian and Wang, Jian-pan

On bialgebra cohomology
Bull. Math. Soc. Belgique XLII (1990), 607-642

Cohomology of infinitesimal quantum groups, I
Tohoku Math. J. 44 (1992), 43-73

Cohomology of quantum groups: the quantum dimension
Canadian Journal of Mathematics 45 (6) (1993), 1276-1298

Paciencier, Samuel and Wang, Hsien-Chung

Commutators in a semi-simple Lie group
PAMS 13 (1962), 907-913
Description: Every element in a semisimple Lie group is a commutator. The proof seems to be similar to the Lie-algebraic case.
Availability: 2034085.pdf

Passman, D.S.

Group rings satisfying a polynomial identity. I
DOI: 10.1016/0021-8693(72)90091-9
J. Algebra 20 (1972), 103-117
MR 44#2849
Zentralblatt: 0226.16015
Description: k[G] satisfies PI iff G has a subgroup H of finite index such that H' is a finite p-group

Group rings satisfying a polynomial identity. II
Pacific J.M. 39 (1971), 425-438

Infinite Group Rings
Marcel Dekker, 1971
MR 47#3500

Group rings satisfying a polynomial identity. III
Proc. Amer. Math. Soc. 31 (1972), 87-90
MR 44#6859
Zentralblatt: 0236.16008

What is a group ring?
DOI: 10.2307/2977018
Amer. Math. Monthly 83 (1976), No.3, 173-185
Description: Nothing about automorphisms.
Availability: 0.pdf

Group Rings, Crossed Products and Galois Theory
AMS
Availability: amazon; Kolkhoz

The Algebraic Structure of Group Rings
URL: http://www.ams.org/bull/1979-01-02/S0273-0979-1979-14618-4/S0273-0979-1979-14618-4.pdf http://projecteuclid.org/euclid.bams/1183544090
Wiley & Sons, 1977
MR 81d:16001
Description: Earlier Passman's results about PI group rings.

Ultraproducts and the group ring semiprimitivity problem
Resenhas IME-USP 2 (1996), 253-261
Zentralblatt: 0987.16501
Availability: hardcopy

The semiprimitivity problem for group algebras of locally finite groups
Israel J.M. 96 (1996), 481-509
Availability: hardcopy

The semiprimitivity problem for twisted group algebras of locally finite groups
PLMS 73 (1996), 323-357
Availability: hardcopy

The Jacobson radical of group rings of locally finite groups
TAMS 349 (1997), N12, 4693-4751
Availability: hardcopy

Simple Lie algebras of Witt-type
URL: http://math.wisc.edu/~passman/abstracts.html http://www.ingentaconnect.com/content/els/00218693/1998/00000206/00000002/art97444
J. Algebra 206 (1998), 682-692
Description: Lie algebras A \tensor D, where A is associative commutative algebras and D is a space of commuting derivations on A.
Availability: hardcopy

Simple Lie color algebras of Witt-type
Preprint
Description: Color counterpart of the previous article. Scheunert's supertrick and its generalization are discussed.
Availability: colorwitt.dvi

Free products in linear groups
Proc. Amer. Math. Soc. 132 (2004), no.1, 37-46
Abstract: Let be a commutative integral domain of characteristic 0, and let be a finite subgroup of PGL_n(R), the projective general linear group of degree n over R. In this note, we show that if n>=2, then PGL_n(R) also contains the free product G*T, where T is the infinite cyclic group generated by the image of a suitable transvection.

Twisted group algebras satisfying a generalized polynomial identity
Preprint
Availability: genpi.dvi

Filtrations in semisimple Lie algebras, III
Description: Usage of Magma for G_2.

Free subgroups in linear groups and group rings
Noncommutative Rings, Group Rings, Diagram Algebras and Their Applications, Contemp. Math. 456 (2008)

Passman, D.S. and Petrogradsky, V.M.

Polycyclic restricted Lie algebras
Availability: polylie.dvi (preprint); 100105977.pdf (published paper)

Patel, J.K. and Read, C.B.

Handbook of the Normal Distribution
Marcel Dekker, 1982
Patel-handDistr.djvu

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Patera, J.

Graded contractions of Lie algebras, their representations and tensor products
Proc. of Symp. Symmetries in Physics, Cocoyoc, Mexico 1991; AIP Conference Proceeding 266, pp. 46-54, 1992.

Patera, Jiri and Pelantova, Edita and Svobodova, Milena

Fine gradings of o(4,C)
J. Math. Phys. 45 (2004), N6, 2188-2198
Description: Fine (i.e those which cannot be refined) gradings of sl(2) x sl(2).

Patera, Jiri and Pelantova, Edita and Twarock, Reidun

Quasicrystal Lie algebras
DOI: 10.1016/S0375-9601(98)00495-2
Phys. Lett. A 246 (1998), 209-213
Description: Witt/Virasoro-like.

Patera, J. and Perena, C.M. and Rodriguez, M.A.

Lie superalgebras and second order automorphisms of classical Lie algebras
Proc. Internat. Coll. Group Theor., Meth. in Phys., Goslar, Germany, Group Theoretical Methods in Physics; eds. H.D. Doebner, P. Nattermann, W. Scherer,World Scientific, Singapore, pp.,193-197, 1996.

Patera, J. and Pogosyan, G. and Winternitz, P.

Graded contractions of the Lie algebra e(2,1)
J. Phys., A: Math. Gen., 32, pp. 805-826, 1999

Patera, J. and Rousseau, C.

Complex orthogonal and symplectic matrices depending on parameters
DOI: 10.1063/1.525424
J. Math. Phys. 23 (1982), N5, 705-714
Availability: JMathPhys_23_705.pdf; hardcopy

Versal deformations of elements of classical Jordan algebras
DOI: 10.1063/1.525869
J. Math. Phys. 24 (1983), N6, 1375-1380
Description: They talk, among all, on quaternionic matrices and Jordan normal forms in gl_m(H) (H - quaternions), but it seems to be a sort of cheating (no non-commutativity of the underlying field is involved).
Availability: JMathPhys_24_1375.pdf; hardcopy

Patera, J. and Rousseau, C. and Schlomiuk, D.

Dimensions of orbits and strata in complex and real classical Lie algebras
DOI: 10.1063/1.525407
J. Math. Phys. 23 (1982), 490-494
Availability: JMathPhys_23_490.pdf

Versal deformations of elements of real classical Lie algebras
J. Phys. A: Math. Gen. 15 (1982), 1063-1086
Availability: jav15i4p1063.pdf

Patera, J. and Sharp, R.T. and Winternitz, P. and Zassenhaus, H.

Invariants of real low dimension Lie algebras
J. Math. Phys. 17 (1976), 986-994
Zentralblatt: 0357.17004

Patera, J. and Twarock, R.

Quasicrystal Lie algebras and their generalizaitons
DOI: 10.1016/S0370-1573(99)00022-8
Phys. Rep. 315 (1999), 241-256
Description: Some Witt-looking amazing Lie algebras.
Availability: science.pdf

Patera, J. and Winternitz, P.

Subalgebras of real three- and four-dimensional Lie algebras
J. Math. Phys. 18 (1977), 1449-1455

Patera, J. and Winternitz, P. and Zassenhaus, H.

Maximal abelian subalgebras of real and complex symplectic Lie algebras
DOI: 10.1063/1.525955
J. Math. Phys. 24 (1983), N8, 1973-1985

Patera, J. and Zasenhaus, Hans

On Lie gradings. I
Lin. Alg. Appl. 112 (1989), 87-159
Availability: hardcopy

Solvable Lie algebras of dimension 4 over perfect fields
DOI: 10.1016/0024-3795(90)90251-7
Lin. Algebra Appl. 142 (1990), 1-17
Availability: 1990-solvable.pdf

The higher rank Virasoro algebras
Comm. Math. Phys. 136 (1991), 1-14

Patodi, V.K.

An analytic proof of Riemann-Roch-Hirzebruch theorem for Kaehler manifolds
J. Diff. Geom. 5(1971), 251-283
Description: Euler-Poincare characteristic of a manifold, related algebraic considerations.
Availability: hardcopy

Patsourakos, Alexandros

Sur la representation adjointe d'une algebre de Lie libre
Comm. Alg. 15 (1987), 2199-2207
Availability: hardcopy

Sur la representation adjointe d'une algebre de Lie libre. II
Ann. Inst. Fourier 44 (1994), No.2, 387-400
Zentralblatt: 0802.17004
Description: g:L(X) -> L(X) is a map on free Lie algebra given by g(x_1 , ... , x_n) = [x_1, [ ... , [x_{n-1}, x_n] .. ]]. Basis of ker(g) is constructed in terms of the Hall basis.

Triple cohomology of Lie algebras
Bull. Greek Math. Soc. 38 (1996), 109-113

A homotopy in the usual cochain complex of free Lie algebras
DOI: 10.1023/A:1007312205995
Lett. Math. Phys. 41 (1997), N4, 391-402
Abstract: ... we construct a natural contracting homotopy in the usual cochain complex of free Lie algebras. As a consequence, we prove that the triple cohomology of Lie algebras coincides with a slightly different form of the standard cohomology theory.

Tensor calculus in the free Lie algebra
DOI: 10.1023/A:1007449917389
Lett. Math. Phys. 45 (1998), N3, 269-276
Abstract: ... we characterize Lie elements and the elements of the kernel of the Lie bracketing from right to left mapping, using tensor calculus tools.

Formulas in the free Lie algebras
DOI: 10.1023/A:1006750118915
Acta Math. Hungar. 89 (2000), no. 4, 277-280

Patterson, E. M.

Generators of linear algebras
DOI: 10.1112/plms/s3-7.1.467
Proc. London Math. Soc. 1957 s3-7, 467-480
Zentralblatt: 0078.02401
Description: Structure of (nonassociative) algebras with restriction between dimension and number of generators. Algebras of genus 1 are described.
Availability: 467.pdf

Paulos, J.A.

A Mathematician Plays The Stock Market
Basic Books, 2003
Availability: math-plays-stock-market.djvu

Pavlovskii, V.V.

Nilpotentnost' nechetnykh differencirovanii v prostykh konechnomernykh superalgebr Lie
Vestnik MGU 2002, N2, 3-7
Description: All inner derivations with odd elements in an finite-dimensional Lie superalgebra are nilpotent only in osp(1,2r) and S^\tilde (3).

Pchelintsev, S. V.

A theorem on height for alternative algebras
DOI: 10.1070/SM1985v052n02ABEH002904
Mat. Sb. 124 (1984), no.4, 557--567
Math. USSR Sbornik 52 (1985), N2, 541-551
MR 86b:17014
Availability: MSB_52_2_A14.pdf

Peckhaus, Volker

Moral Integrity during a Difficult Period: Beth and Scholz
Philosophia Scientiae (Nancy) 3 (4) (1998/1999), 151-173
Description: Philosophy of mathematics during Nazi times.
Availability: beth.pdf

Pedersen, Niels Vigand

Orbits and primitive ideals of solvable Lie algebras
Math. Ann. 298(1994), 275-326
Description: Some general reasonings about symmetric bilinear forms on Lie algebras.
Availability: Gottinger archive

Pellegrini, Fabien

Real forms of complex Lie superalgebras and complex algebraic supergroups
Pacific J. Math. 229 (2007), no. 2, 485--498

Pendergrass-Rice, Cayley

Extending a theorem of Herstein
arXiv:0710.5545
Description: Herstein's theorem on relationship between simple/prime associative rings (with involution) and Lie rings is generalized to just infinite algebras (i.e. algebras all whose homomorphic images are finite-dimensional).

Penkava, Michael and Vanhaecke, Pol

Hochschild cohomology of polynomial algebras
DOI: 10.1142/S021919970100041X
Comm. Contemp. Math. 3 (2001), No. 3, 393-402
Description: An alternative (simple) computation of H^{2,3}(P,P).
Availability: www10a.ps

Deformation quantization of polynomial Poisson algebras
Preprint
Availability: www10b.ps

Penkov, Ivan and Strade, Helmut

Locally finite Lie algebras with root decomposition
Arch. Math. 80 (2003), N5, 478 - 485
Zentralblatt: 1035.17033

Penkov, Ivan and Zuckerman, Gregg

Generalized Harish-Chandra Modules: A New Direction
math.RT/0310140

Penney, Richard C.

The theory of ad-associative Lie algebras
Pacific J. Math. 99 (1982), 459-472
MR 658075
Zentralblatt: 0501.17004
Description: Finite-dimensioanl Lie algebras L for which ad(L) is associative. Such algebras are solvable.

Penrose, Roger

The Road to Reality
Jonathan Cape, London, 2004
Review: Notices AMS, June/July 2006, 661- Ferment Magazine, by Roy Lisker
Availability: 2004-road.pdf; hardcopy

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Perchik, James

Cohomology of Hamiltonian and related formal vector field Lie algebras
Topology 15(1976), N4, 395-404
Availability: science.pdf; hardcopy

Perelomov, A.M.

Integriruemye sistemy klassicheskoi mekhaniki i algebry Lie
R&C Dynamics, 2002 (in Russian); paperback, small format, 237 pp.
Availability: hardcopy (book)

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Perera, Francesc and Molina, Mercedes Siles (=Siles Molina, Mercedes)

Associative and Lie algebras of quotients
Publ. Mat. 52 (2008), no. 1, 129--149
arXiv:math.RA/0509510
Description: Algebra of quotient of a Lie algebras is studied and its relations with an associative case.

Strongly nondegenerate Lie algebras
DOI: 10.1090/S0002-9939-08-09558-0
Proc. Amer. Math. Soc. 136 (2008), 4115-4124
arXiv:0802.1591
Description: Various properties of Der(A) assuming properties of A (primeness, etc.).

Peresi, L. A.

A basis of identities for Bernstein algebras
Int. J. Math. Game Theory Algebra 14 (2004), no. 3, 179--188

Perez-Izquierdo, Jose M.

Division composition algebras through their derivation algebras
DOI: 10.1016/j.jalgebra.2006.06.014
J. Algebra 303 (2006), N1, 1-29

Permyakov, D.S.

Derivations of classical Lie algebras over the field of characteristic 2
Vestnik NNGU Ser. mat. 2005, Vyp. 1(3), 123-134 (in Russian)

Pesic, Peter

Abel's Proof. An Essay on the Sources and Meaning of Mathematical Unsolvability
The MIT Press, 2003; hardcover with dustjacket, 213 pp.
Availability: hardcopy

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Pestov, Vladimir

On a `super' version of Lie's third fundamental theorem
Letters in Math. Physics 18 (1989), 27-33

A correspondence between finite-dimensional Lie superalgebras and supergroups
Extracta Mathematicae 7 (1992), 119--125

Peterson, I.

The Mathematical Tourist
Freeman and Co., New York, 1988; paperback, 240 pp.
Availability: hardcopy (book)

Peterson, Dale H. and Kac, Victor G.

Infinite flag varieties and conjugacy theorems
Proc. Nat. Acad. Sci. USA 80 (1983), no. 6, 1778-1782
MR 84g:17017
Description: Automorphisms of Kac-Moody and loop algebras.
Availability: 1778.pdf

Peterson, Michael and Monico, Chris

F_2 Lanczos revisited
DOI: 10.1016/j.laa.2007.09.016
Lin. Algebra Appl. 428 (2008), N4, 1135-1150
Availability: hardcopy

Petersson, Holger P.

Max Koecher's work on Jordan algebras
Jordan Algebras, deGruyter, 1994, 187-195
Availability: hardcopy

The classification of two-dimensional nonassociative algebras
Resultate Math. 37 (2000), 120-154

Petersson, Holger P. and Racine, Michel L.

Cubic Subfields of Exceptional Simple Jordan Algebras
PAMS 91(1984), No.1, 31-36
Availability: JSTOR

Octonion algebras obtained from associative algebras with involution
Proc. Amer. Math. Soc. 130(2002), no.6, 1563-1572

Petersson, Holger P. and Scherer, Matthias

The number of nonisomorphic two-dimensional algebras over a finite field
Results Math. 45 (2004), no. 1-2, 137--152

Petit, Toukaiddine

On the strong rigidity of solvable Lie algebras
De Concini, Corrado (ed.) et al., Noncommutative algebra and geometry. Selected papers of a conference in honor of Z. Borevich, St. Petersburg, Russia. Boca Raton, FL: CRC Press, Lecture Notes in Pure and Applied Mathematics 243, 162-174 (2005).
Zentralblatt: 1099.17012 (me)
Availability: hardcopy

Generalized derivation tower theorem of Lie algebras
math.RT/0503370

Petit, Toukaiddine and Van Oystaeyen, Freddy

Note on the generalized derivation tower theorem for Lie algebras
Abelian groups, rings, modules, and homological algebra, Lect. Notes Pure Appl. Math., 249, Chapman & Hall/CRC, 2006, 251--263

On the generalized enveloping algebra of a color Lie algebra
DOI: 10.1007/s10468-007-9048-3
arXiv:math.RA/0512574
Algebras and Representation Theory Volume 10, Number 4 / August, 2007 Pages 367-378

Petkovsek, M. and Wilf, H. and Zeilberger, D.

A=B
Description: Automatic proof of binomial (combinatorial?) identities.

Petracci, Emanuela

Universal representations of Lie algebras by coderivations
Bull. Sci. Math. 127(2003), N5, 439-465
math.RT/0303020
Abstract: A class of representations of a Lie superalgebra (over a commutative superring) in its symmetric algebra is studied. As an application we get a direct and natural proof of a strong form of the Poincar�-Birkhoff-Witt theorem, extending this theorem to a class of nilpotent Lie superalgebras. Other applications are presented. Our results are new already for Lie algebras.

Petravchuk, Anatolii P.

Lie algebras, decomposable into a sum of an abelian and a nilpotent subalgebra
DOI: 10.1007/BF01061314
Ukr. Math. J. 40 (1988), N3, 331-334
Zentralblatt: 0653.17003
Availability: 1988-lie.pdf; hardcopy

The solubility of a Lie algebra which decomposes into a direct sum of an abelian and a nilpotent subalgebra
DOI: 10.1007/BF01058694
Ukr. Math. J. 43 (1991), N7-8, 920-924
Zentralblatt: 0747.17011
Description: Infinite-dimensional algebras, p not 2.
Availability: 1991-solubility.pdf

On a sum of two Lie algebras with finite dimensional commutant
Ukr. Math. J. 47 (1995), N8, 1244-1252
Zentralblatt: 0934.17002
Description: At one place (near the end) Weisfeiler's filtration is used!
Availability: hardcopy

Triple sums of abelian Lie algebras
Mat. Stud. 8, No.1, 11-14 (1997)
Zentralblatt: 0954.17005

On the sum of a commutative and a Lie nilpotent associative ring
Vestnik Kiev. Univ. 1 (1998), 33-35 (in Ukraininan)
Zentralblatt: 0954.16003
Description: An associative ring that is representable as the sum of commutative and Lie nilpotent subrings, is Lie solvable.

Lie algebras with complemented one-dimensional subalgebras
Vestnik Kiev. Univ. 3 (1999), 32-37 (in Ukraininan)
Zentralblatt: 0947.17001

Locally finite Lie algebras with complemented one-dimensional subalgebras
Mat. Stud. 11 (1999), No.2, 135-140
Zentralblatt: 0954.17006

On the sum of an almost abelian Lie algebra and a Lie algebra finite-dimensional over its center
DOI: 10.1007/BF02591706
Ukr. Math. J. 51 (1999), No.5, 707-715
Zentralblatt: 0967.17005
Availability: hardcopy

On derived length of the sum of two nilpotent Lie algebras
Visn. Kyi"v. Univ., Ser. Mat. Mekh. 6 (2001), 53-56 (in Ukrainian)
Zentralblatt: 0985.17016

Associative rings generated by two nilpotent subrings
Visn., Ser. Fiz.-Mat. Nauky, Ky\" iv. Univ. Im. Tarasa Shevchenka 2001, No.1, 54-56 (Ukrainian)
Zentralblatt: 0979.16011
Description: Associative ring that is represented as A + B + AB for nilpotent subrings A,B, is nilpotent. This generalizes the classical result of Kegel.

On behavior of solvable ideals of Lie algebras under outer derivations
arXiv:0808.3262

Petravchuk, Anatolii P. and Bilun, Svitlana V.

Finite-dimensional Lie algebras with abelian complex structures
Visn. Kiiv. Univ. Ser. Fiz.-Mat. Nauki 2003, no.1, 42--44

On orthogonal operators on finite dimensional Lie algebras
Visn., Ser. Fiz.-Mat. Nauky, Ky\"iv. Univ. Im. Tarasa Shevchenka 2003, No. 3, 60-64 (Ukrainian)
Zentralblatt: 1122.17301
Description: Finite-dimensional Lie algebras admitting a linear operator T with [Tx,Ty]=[x,y] and without eigenvalues 1 and -1, are solvable.

Petravchuk, A. P. and Maksimenko, D. V.

On the sum of an abelian Lie algebra and a Lie FC-algebra with a nontrivial center
Third International Algebraic Conference in the Ukraine, 100--105, Natsional. Akad. Nauk Ukraini, Inst. Mat., Kiev, 2002

Petrich, Mario

Rings and Semigroups
LNM 380 (1974); 182 pp.
Availability: hardcopy (book); absent on amazon

Lectures on Semigroups
Wiley, 1977, 239 pp.

Completely Regular Semigroups
Wiley, 1999

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Petrogradsky, V.M.

Existence of identities in the restricted enveloping algebra
DOI: 10.1007/BF01137064
Math. Notes 49 (1991), N1, 60-66
MR 92d:17012
Description: When a restricted envelope of a (restricted) Lie algebra is PI?

Growth of polynilpotent varieties of Lie algebras and rapidly growing entire functions
DOI: 10.1070/SM1997v188n06ABEH000232
1997 Sb. Math. 188 913-931
MR 1479133
Zentralblatt: 0890.17002
Availability: MSB_188_6_A06.pdf

Witt's formula for restricted Lie algebras
DOI: 10.1016/S0196-8858(02)00533-X
Adv. Appl. Math. 30 (2003), N1-2, 219-227
Description: Dimensions of homogeneous components for free Lie superalgebras and free Lie p-algebras.

Examples of self-iterating Lie algebras
DOI: 10.1016/j.jalgebra.2005.09.005
J. Algebra 302 (2006), N2, 881-886
Description: Restricted Lie algebras with some growth properties.

Petrogradsky, V. M. and Razmyslov, Yu. P. and Shishkin, E. O.

Wreath products and Kaluzhnin-Krasner embedding for Lie algebras
Proc. Amer. Math. Soc. 135 (2007), 625-636
MR 2008a:17020
Description: An arbitrary extension of Lie algebras 0 -> H -> L -> G -> 0 can be embedded into the wreath product L -> H wr G, and wreath product is an universal object which contains all such extensions.
Availability: S0002-9939-06-08502-9.ps

Petrovic, Zoran

Nonsingular bilinear maps, spaces of matrices, immersions and embeddings
Proceedings of the Conference Contemporary geometry and Related Topics, University of Belgrade, 2006, 427-
Description: A surevy of results about dimension of spaces of matrices of given rank, or of matrices of rank not less than a fixed number, over R and C.

Pevzner, M. and Torossian, Ch.

Isomorphisme de Duflo et la cohomologie tangentielle
DOI: 10.1016/j.geomphys.2004.03.001
J. Geom. Phys. 51 (2004), N4, 486-505
arXiv:math.QA/0310128
Description: H^*(g,U(g)) = H^*(g,S(g)) for a finite-dimensional Lie algebra g, p=0.

Pfautsch

Ext^1 for Frobenius kernels of SL_2
Comm. Alg. 13(1985), 169-179
Availability: hardcopy

Pfeifer, Walter

The Lie Algebras su(N), an Introduction
2003

Pflaum, M. and Posthuma, H. and Tang, X.

Cyclic cocycles on deformation quantizations and higher index theorems
arXiv:0805.1411
Description: Cyclic cohomology of the Weyl algebra.

Pham Huu Tiep

IRREDUCIBLE ORTHOGONAL DECOMPOSITIONS IN LIE ALGEBRAS
DOI: 10.1070/SM1991v068n01ABEH002103
1991 Math. USSR Sb. 68 257-275
Description: Some special type (irreducible) orthogonal decompositions for simple Lie algebras (related to the Winnie-the-Pooh problem).
Availability: MSB_68_1_A13.pdf

Pham, D.T. and Karaboga, D.

Intelligent Optimization Techniques. Genetic Algorithms, Tabu Search, Simulated Annealing and Neural Networks
2nd printing, Springer, 2000; hardcover, 302 pp.
Availability: hardcopy (book)

Piacentini Cattaneo, G. M. and Pittaluga, M.

Nonassociative polynomial identities, Young tableaux and computers
ACM SIGSAM Bulletin Volume 22 , Issue 2 (April 1988) Pages: 17 - 26
Availability: p17-piacentini.pdf

Pianzola, Arturo

Line bundles and conjugacy theorems for toroidal Lie algebras
Comptes Rendus Math. Acad. Sci. (Canada) 22(2000), N3
MR 2001d:17004
Abstract: We link the Picard group of SpecR to the question of conjugacy of maximal abelian diagonalizable subalgebras of R \otimes g.
Availability: author's homepage (file CRlines.pdf) (?)

Affine Kac-Moody Lie algebras as torsors over the punctured line
Indag. Math. 13 (2002), no. 2, 249-257
math.RT/0203277
Description: Generalization of (twisted) affine Lie algebras extended over arbitrary algebra L.

Automorphisms of toroidal Lie Algebras and their central quotients
J. Algebra and its Applications 1 (2002), N1
Description: Automorphisms group of g \otimes R, g simple classical, R with trivial Picard group; relationship between automorphisms of a Lie algebra and of automorphisms of its universal central extension.
Availability: PianzolaJAA.pdf, hardcopy

Locally trivial principal homogeneous spaces and conjugacy theorems for Lie algebras
DOI: 10.1016/S0021-8693(03)00399-5
J. Algebra 275 (2004), no. 2, 600--614
math.RT/0304068
Abstract: For g a split semisimple Lie algebra over a field of characteristic 0, we link locally trivial principal homogeneous spaces over Spec(R) to the question of conjugacy of maximal abelian diagonalizable subalgebras of g \otimes R.

Twisted loop algebras and Galois cohomology.
Groups, rings and group rings, 293--304, Lect. Notes Pure Appl. Math., 248, Chapman & Hall/CRC, Boca Raton, FL, 2006

Pianzola, Arturo and Prelat, Daniel and Sun, Jie

Descent constructions for central extensions of infinite dimensional Lie algebras
DOI: 10.1007/s00229-006-0053-3
Manuscr. Math. 122 (2007), N2, 137-148
arXiv:0711.3799
Abstract: We use Galois descent to construct central extensions of twisted forms of split simple Lie algebras over rings.

Pichereau, Anne

Poisson (co)homology and isolated singularities
DOI: 10.1016/j.jalgebra.2005.10.029
J. Algebra 299 (2006), N2, 747-777
arXiv:math.QA/0511201
Description: Poisson cohomology of some Poisson algebras based on polynomials.

Formal deformations of Poisson structures in low dimensions
arXiv:0806.2349

Pichereau, Anne and Van de Weyer, Geert

Double Poisson cohomology of path algebras of quivers
DOI: 10.1016/j.jalgebra.2007.09.021
arXiv:math.RA/0701837
J. Algebra 319 (2008), N5, 2166-2208

Pickel, P.F.

Rational cohomology of nilpotent groups and Lie algebras
DOI: 10.1080/00927877808822253
Comm. Algebra 6 (1978), N4, 409-419
Description: Cohomology of a nilpotent group and associated, via Malcev corresponcence, nilpotent Lie algebras, coincide.
Availability: 780153670_content.pdf

Pickert, G�nter

Dreidimensionale assoziative nichtkommutative Algebren
DOI: 10.1006/jabr.2000.8550
Journal of Algebra Volume 234, Issue 2, 15 December 2000, Pages 280-290

Pickrell, Doug

$H^4(BK,Z)$ and Operator Algebras
Journal of Lie Theory Vol. 14, No. 1, pp. 199--213 (2004)
Abstract: There is a well-known interpretation of group cohomology in terms of (generalized) group extensions. For a connected semisimple compact Lie group $K$, we prove that the extensions corresponding to classes in $H^4(BK,\Z)$ can be interpreted in terms of automorphisms of a pair consisting of a type $II_1$ von Neumann algebra and a Cartan subalgebra.

Pierce, R.S.

Associative Algebras
Mir, 1986 (Russian translation from Springer, 1982); hardcover, 541 pp.
MR 84c:16001
Availability: hardcopy (book); amazon; Kolkhoz (in Russian)

Pikhtilkov, S. A.

On special Lie algebras
DOI: 10.1070/RM1981v036n06ABEH003129
Uspekhi Mat. Nauk 36 (1981), no.6, 225-226
MR 83g:17004
Zentralblatt: 0482.17007
Description: A question, whether a homomorphic image of a special Lie algebra, is special, is considered.
Availability: hardcopy

On locally nilpotent ideals of special Lie algebras
Comm. Alg. 29 (2001), N9, 3781-3786
Availability: 100105974.pdf

On locally nilpotent radical of special Lie algebras
Fund. Prikl. Mat. 8 (2002), N3, 769-782
Zentralblatt: 1022.17003
Description: Attempt of a generic structure theory for infinite dimensional Lie algebras with various finitness/nilpotency conditions. Many interesting facts about special Lie algebras are cited.
Availability: k02311.ps; hardcopy

Structural theory of special Lie algebras
Izv. Tul. Gos. Univ. Ser. Mat. Mekh. Inform. 8 (2002), no. 1, Matematika, 96--11 (in Russian)

Structural theory of special Lie algebras
DOI: 10.1007/s10958-006-0222-7
J. Math. Sci. 136 (2006), N4, 4090-4115
Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 118, Algebra, 2004
Availability: hardcopy

Pikhtilkov, S. A. and Polyakov, V.

Artinal special Lie superalgebras
Bul. Acad. Stiinte Repub. Mold. Mat. 2004, no. 1, 116--119

Pillay, Anand

Model theory of algebraically closed fields
Model Theory and Algebraic Geometry (ed. E.Bouscaren), LNM 1696 (1998), 61-84
Description: Model-theoretic approach to algebraic groups
Availability: hardcopy

Model theory
Notices AMS, December 2000

Pin, J.-E.

Finite senigroups as cetgories, ordered semigroups or compact semigroups
Semigroup Theory and Applications (ed. K.H. Hofmann and M.W. Mislove), LMS Lect. Notes Ser. 231, Cambridge Univ. Press, 1996, 107-
Description: Varieties. Interesting.
Availability: hardcopy (book)

Pinczon, George

Noncommutative deformation theory
Lett. M. Phys. 41 (1997), 101-117

On two theorems about symplectic reflection algebras
DOI: 10.1007/s11005-007-0190-y
arXiv:math.RT/0612690
Letters in Mathematical Physics Volume 82, Numbers 2-3 / December, 2007 Pages 237-253
Abstract: We give a new proof and an improvement of two Theorems of J. Alev, M.A. Farinati, T. Lambre and A.L. Solotar : the first one about Hochschild cohomology spaces of some twisted bimodules of the Weyl algebra W and the second one about Hochschild cohomology spaces of the smash product G * W (G a finite subgroup of SP(2n)), and as an application, we then give a new proof of a Theorem of P. Etingof and V. Ginzburg, which shows that the Symplectic Reflection Algebras are deformations of G * W (and, in fact, all possible ones).

Pinczon, Georges and Ushirobira, Rosane

Supertrace and superquadratic Lie structure on the Weyl algebra, and applications to formal inverse Weyl transform
Lett. Math. Phys. 74, N3, 263-

The Weyl algebra is a superquadratic Lie superalgebra
arXiv:math.RT/0507092
Description: Lie superalgebra structure of Weyl algebra.

New applications of graded Lie algebras to Lie algebras, generalized Lie algebras, and cohomology
J. Lie Theory 17 (2007), no. 3, 633--667
arXiv:math.RT/0507387
Abstract: We revisit graded Lie algebras related to Deformation Theory, examining among others, Gerstenhaber, Gerstenhaber-Nijenhuis, Schouten and super Poisson brackets. We give new applications to identities of standard polynomials, deformation theory of quadratic Lie algebras, cyclic cohomology of quadratic Lie algebras, generalized Lie algebras, generalized Poisson brackets and so on.

Pinkus, A.Z. and Winitzky, S.

YACAS: A Do-it-yourself Symbolic Algebra Environment
LNCS 2385 (2002), 332-

Pinl, M.

Kollegen in einer dunklen Zeit
Jahresber. Deutsch. Math.-Verein. 71 (1969), 167-288; (1970/71), 165-189; 73 (1971/72), 153-208; 75 (1973/74), 160-208
Description: Mathematicians at Nazi times.

Pinnock, Christopher John Edward

Supersolubility and finitary groups
PhD Thesis, U. of London, 2000
Description: "... We generalize Platonov's theorems on linear groups of finite Pruefer rank and linear groups satisfying non-trivial laws to cretian finitary skew linear groups". Also some genralizations of Tits alternative are mentioned (Chapter 3). Some results from here are published in subsequent author's papers, see URL.
Availability: thesis.pdf

Lawlessness and rank restrictions in certain finitary groups
Preprint
Description: This is a paper extracted from the author's PhD thesis (see above).
Availability: lawlessness-and-rank-restrictions.pdf; author's homepage ?

Pinus, A. G. and Vazhenin, Yu. M.

Elementary classification and decidability of theories of derived structures
DOI: 10.1070/RM2005v060n03ABEH000847
Russian Math. Surveys 60(2005), N3, 395-432
Availability: rm_60_395.pdf

Piontkovskii, D.I. (= Piontkovsky)

On Hilbert series and the homology of PI-algebras
DOI: 10.1070/SM1998v189n11ABEH000373
Math. Sbornik 189 (1998), N11, 1685-1700
MR 1685921
Zentralblatt: 0932.16023
Availability: 1998-hilbert.pdf

Growth and relations in graded rings
arXiv:math.RA/9903030
Description: A version of Golod-Shafarevich theorem for graded associative algebras in terms of Hilbert series.

On graded algebras of global dimension 3
DOI: 10.1070/IM2001v065n03ABEH000339
Izvestiya Math. 65 (2001), 557-568
Description: Relationship between associative algebra A = F/I (F - free algebra) and algebra F/I + I/I^2 + ... Usage of Baer formulae. Seemingly interesting homological considerations.
Availability: piont.pdf

Koszul algebras and their ideals
Funct. Anal. Prilozh. 39 (2005), N2, 47-60
(me)
Availability: hardcopy

Graded algebras and their differential graded extensions
DOI: 10.1007/s10958-007-0137-y
J. Math. Sci. 142 (2007), N4, 2267-2301
Description: A survey. Homological description of extensions and deformations of PI-algebras. Homological description of Groebner bases.
Availability: hardcopy

Piontkovski, Dmitri and Silvestrov, Sergei

Cohomology of 3-dimensional color Lie algebras
DOI: 10.1016/j.jalgebra.2006.11.008
arXiv:math.KT/0508573
J. Algebra 316 (2007), N2, 499-513
Abstract: We develop the cohomology theory of color Lie superalgebras due to Scheunert--Zhang in a framework of nonhomogeneous quadratic Koszul algebras. In this approach, the Chevalley--Eilenberg complex of a color Lie algebra becomes a standard Koszul complex for its universal enveloping algebra. As an application, we calculate cohomologies with trivial coefficients of 3-dimensional color Lie superalgebras.

Piotrovskii, R.G. and Bektaev, K.B. and Piotrovskaya, A.A.

Matematicheskaya lingvistika
Vysshaya Shkola, Moscow, 1977 (in Russian); hardcover
Availability: hardcopy (book)

Piper, W. Stephen

Algebraic deformation theory
J. Diff. Geom. 1(1967), 133-168
Availability: hardcopy

Algebras of matrices under deformation
J. Diff. Geom. 5(1971), 437-449
Description: Examples of deformations of associative algebra of upper triangular matrices.

Pirashvili, Teimuraz

On Leibniz homology
Ann. Inst. Fourier 44 (1994), 401-411
Description: Spectral sequence abutting to Leibnitz homology. Relationship between Chevalley-Eilenberg and Leibnitz homology. Symmetric invariant bilinear forms are involved. Vanishing of leibniyz homology of classical semisimple Lie algebras.
Availability: hardcopy

The Euler-Poincare characteristic of a Lie algebra
J. Lie Theory 8 (1998), 429-431
Description: The Euler-Poincare characetristic is dim H^0(L,M) - H^1(L,M) + H^2(L,M) - .... It is proved that if either p=0 or L is not perfect, Euler-Poincare char. is 0.
Availability: hardcopy

Andr�-Quillen homology via functor homology
Proc. Amer. Math. Soc. 131 (2003), 1687-1694

Algebra cohomology over a commutative algebra revisited
arXiv:math.KT/0309184
Abstract: The aim of this paper is to give a relatively easy bicomplex which computes the Shukla, or Quillen cohomology in the category of associative algebras over a commutative algebra $A$, in the case when $A$ is an algebra over a field.

Piron, C.

Foundations of Quantum Physics
W. A. Benjamin, 1976
Description: Quantum mechanics is formulated in the language of (quantum) logic and projective geometry.

Pistone, Giovanni and Riccomagno, Eva and Wynn, Henry P.

Algebraic Statistics. Computational Commutative Algebra in Statistics
Chapman & Hall/CRC, 2001, 184pp.
Description: Including Groebner bases.
Availability: google books

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Pistone, G. and Sempi, C.

An infinite dimensional geometric structure on the space of all the probability measures equivalent to a given one
(1995) Ann. Statist. 33, 1543-1561

PISTONE, GIOVANNI and WYNN, HENRY P.

Generalised confounding with Gr�bner bases
DOI: 10.1093/biomet/83.3.653
Biometrika 1996 83(3):653-666

Pitassi, Toniann

Unsolvable systems of equations and proof complexity
Documenta Math. Extra Vol. ICM 1998 III, 451-460
Description: Propositional formulas reformulated as (systems of) polynomial equations.
Availability: hardcopy

Pitt, Loren D.

Positively Correlated Normal Variables are Associated
The Annals of Probability, Vol. 10, No. 2 (May, 1982), pp. 496-499
Availability: 00911798_di983796_98p0100u.pdf

Piva, Margot and Holgate, Philip

The eigenvectors of a finite population model
Ann. Hum. Genet. 41 (1977), 103-106
Zentralblatt: 0365.92029

Platonov, V.P.

Engelevy elementy i radikal v PI-algebrakh i topologicheskikh gruppakh DAN SSSR 161 (1965), N2, 289-291
Availability: hardcopy

The Frattini subgroup of linear groups and finite approximability
Sov. Math. Dokl. 7 (1966), N6, 1557-1560
MR 35#2971
Availability: hardcopy

The theory of algebraic linear groups and periodic groups
Izv. AN SSSR 30 (1966), 573-620
AMS Transl. 69 (1968), 61-110
MR 0199279
Zentralblatt: 0146.04405
Description: Wehrfritz: a wealth of diverse and interesting results, many examples.

Linear groups with identiy relations
Dokl. Akad. Nauk BSSR 11 (1967), N7, 581-582 (in Russian)
Zentralblatt: 0252.20036
Description: A linear group satisfies a nontrivial identity iff it is a finite extension of a solvable group.
Availability: hardcopy

Some remarks on linear groups
DOI: 10.1007/BF01110820
Math. Notes 4 (1968), N6, 873-874
Availability: 1968-some.pdf

On a problem of Malcev
DOI: 10.1070/SM1969v008n04ABEH001124
Math USSR Sbornik 8 (1969), N4, 599-602
Description: A linear group over a field is a group of finite rank if and only if it is a finite extension of a solvable group of finite rank (rank is a maximum of a number of generators of all proper subgroups).
Availability: MSB_8_4_A05.pdf; hardcopy

Algebraic groups
J. Math. Sci. 4 (1975), N5, 463-482
Alg. Top. Geom., Vol. 11, VINITI, 5-
Description: A VINITI survey.
Availability: p141281411n75p17.pdf

The arithmetic theory of algebraic groups
DOI: 10.1070/RM1982v037n03ABEH003230
Russ. Math. Surv. 37 (1982), No.3, 1-62
MR 659426
Zentralblatt: 0513.20028
Description: A survey.

Platonov, V.P. and Rapinchuk, A.S.

Algebraic groups
DOI: 10.1007/BF02106806
J. Math. Sci. 31 (1985), N3, 2939-2973
Alg. Top. Geom., Vol. 21, VINITI, 1983, 80-
Description: A VINITI survey.
Availability: p841708uu33qr615.pdf

Algebraic Groups and Number Theory
Academic Press, 1994 (translation from Russian, Nauka, 1991)
Description: Including Galois cohomology and forms.
Availability: Kolkhoz; 1991-alg.djvu

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Platonov, V.P. and Yanchevskii, V.I.

Finite-dimensional division algebras
Algebra IX, Encyclopaedia of Mathematical Sciences, Springer, Vol. 77, 1996, 121-233
Availability: algebra-9.djvu (whole book); Kolkhoz (Russian edition, VINITI); VRII 510.3 Enc

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Plotkin, Boris I.

Algebraic sets of elements in groups and Lie algebras (in Russian)
UMN 13 (1958), N6, 133-138
MR 0103223
Zentralblatt: 0099.02204
Description: Seems to be not very interesting.

Gruppy avtomorfizmov algebraicheskikh sistem
Nauka, 1966 (in Russian)
Availability: aut-groups-alg-systems.djvu; absent on ozon; Kolkhoz

Universal Algebra, Algebraic Logic and Databases
Nauka, 1991 (in Russian)
Availability: Kolkhoz

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General theory of groups
DOI: 10.1007/BF01084470
J. Sov. Math. 1 (1973), 527-570
Alg. Top. Geom. 1970, VINITI, 5-
Description: A VINITI survey.
Availability: r433001532w68763.pdf

Galois theory of databases
DOI: 10.1007/BFb0082013
LNM 1352 (1988), 147-161
Availability: hardcopy

Universal Algebra, Algebraic Logic and Databases
Kluwer, 1994
Availability: TUDelft (In - 69F41 Plot); databases.djvu (Russian original)

Varieties of algebras and algebraic varieties
Israel J. Math. 96 (1996)

Algebra, categories, and databases
Handbook of Algebra (ed M. Hazewinkel), Vol. 2, North-Holland, 2000, 79-
Availability: vol2.djvu (whole book)

Seven lectures on the universal algebraic geometry
arXiv:math.GM/0204245, 87 pages
Hebrew University, Institute of mathematics, Preprint 1-2000

Algebras with the same (algebraic) geometry
Proc. Steklov Inst. Math. 242 (2003), 165-
arXiv:math.GM/0210194

Algebraic logic, varieties of algebras and algebraic varieties
arXiv:math.GM/0312420, 62 pp.

Geometrical equivalence, geometrical similarity and geometrical compatibility of algebras
arXiv:math.GM/0312427

Algebraic geometry in first order logic
arXiv:math.GM/0312485

Problems in algebra inspired by universal algebraic geometry
DOI: 10.1007/s10958-006-0390-5
Fundamentalnaya i Prikladnaya Matematika 10 (2004), N3, 181--197
J. Math. Sci. 139 (2006), N4, 6780-6791
arXiv:math.GM/0406101

Some results and problems related to universal algebraic geometry
DOI: 10.1142/S0218196707003986
Intern. J. Algebra Comput. 17 (2007), N5/6, 1133-1164

Plotkin, B.I. and Gringlaz, L.Ya. and Gvaramiya, A.A.

Elementy algebraicheskoi teorii avtomatov
Vysshaya Shkola, Moscow, 1994 (in Russian); paperback, 191 pp.
Availability: hardcopy (book); absent on ozon

Plotkin, B. and Plotkin, T.

Lect. Notes Computer Science 2138(2001), 35-
Abstract: This paper considers interrelations between universal algebra, algebraic logic, geometry and computer science. The key idea of the paper is to show that problems, coming from computer science, require introducing of highly non-trivial mathematical structures. On the other hand, algebraic models in computer science give deeper understanding of problems essence. This general idea is illustrated on the example of knowledge bases. Theorems concerning the knowledge base equivalence problem are formulated.

Geometrical aspect of databases and knowledge bases
Algebra Universalis 46(2001), N1-2, 131-161

An algebraic approach to knowledge base models informational equivalence
math.GM/0312428
Acta Applicandae Mathematicae Volume 89, Numbers 1-3 December 2005 Pages: 109 - 134

Plotkin, T.L. and Plotkin, B.I. and Kraus, S.

Algebraic logic in database state description (in Russian)
Fund. Prikl. Mat. 2(1996), 875-910
Availability: fpm96309.ps

Plotkin, Eugene and Semenov, Andrei and Vavilov, Nikolai

Visual basic representations. An atlas
Intern. J. of Algebra and Computation 8(1998), No. 1, 61-95
Abstract: We depict the weight diagrams (alias, crystal graphs) of basic and adjoint representations of complex simple Lie algebras/algebraic groups and describe some of their uses.

Plotkin, Boris and Zhitomirski, Grigori

On automorphisms of categories of universal algebras
arXiv:math.CT/0411408

Automorphisms of categories of free algebras of some varieties
DOI: 10.1016/j.jalgebra.2006.07.028
J. Algebra 306 (2006), N2, 344-367
arXiv:math.RA/0501331

Some logical invariants of algebras and logical relations between algebras
DOI: 10.1090/S1061-0022-08-01023-6
Algebra i Analiz, tom 19 (2007), nomer 5
St. Petersburg Math. J. 19 (2008), 829-852

Poggio, Tomas and Smale, Steve

The mathematics of learning: dealing with data
Notices AMS, May 2003, 537-544
Availability: hardcopy

Pogorelov, A.V.

Elementarnaya geometriya
Nauka, 1974 (in Russian)
Availability: hardcopy (book)

Pogosyan, George and Sissakian, Alexey and Winternitz, Pavel

Separation of variables and Lie algebra contractions. Applications to special functions
arXiv:math-ph/0310011
Phys. Part. Nuclei 33 (2002), 235-276
Abstract: A review is given of some recently obtained results on analytic contractions of Lie algebras and Lie groups and their applications to special function theory.

Pogrebkov, A. K.

Commutator identities on associative algebras and the integrability of nonlinear revolution equations
DOI: 10.1007/s11232-008-0035-6
Theoretical and Mathematical Physics Volume 154, Number 3 / March, 2008 Pages 405-417
Description: Interesting general identities in arbitrary associative algebras including commutators and powers of elements.

Poguntke, Detlev

The theorem of Lie and hyperplane subalgebras of Lie algebras
DOI: 10.1007/BF00181299
Geom. Dedicata 43 (1992), N1, 83-91
Description: Further development of radical (intersection of all subalgebrs of codimension 1) introduced by Hoffman.

Pohl, R.W.

Einfürung in die Mechanik und Akustik
2nd ed., Springer, 1931; hardcover, 251 pp.
Availability: hardcopy (book)

Einfürung in die Elektrizitätslehre
3rd ed., Springer, 1931; hardcover, 264 pp.
Availability: hardcopy (book)

Einfürung in die Optik
Springer, 1940; hardcover, 320 pp.
Availability: hardcopy (book)

Poincaré, H.

Poslednie raboty A. Poincare
R & C Dynamics, 2001 (in Russian); paperback, 207 pp.
Availability: absent on amazon; hardcopy (book); Kolkhoz

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Point, Francoise

Groups with identities
DOI: 10.1016/0168-0072(89)90060-2
Ann. Pure Appl. Logic 45 (1989), No.2, 171-188
Zentralblatt: 0697.20013
Description: Characterization of groups none of whose elementary extensions contain a free monoid in two variables.
Availability: 1989-groups.pdf

Ultraproducts and Chevalley groups
DOI: 10.1007/s001530050131
Arch. Math. Logic 38 (1999), N6, 355 - 372
Zentralblatt: 0921.03008
Description: The functors of taking a Chevalley group (over field) and ultraproducts commute.
Availability: NXXFR0D9UJHBUNGV.pdf

Poizat, Bruno

A Course in Model Theory. An Introduction to Contemporary Mathematical Logic
URL: http://www.math.wisc.edu/~lempp/poizat/poizat.html http://www.ksu.ru/eng/departments/f5/K2/index.php?id=7
Springer, 2000, 443 pp.

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Stable Groups
AMS, 2001 (translated from French, Nur Al-Mantiq Wal-Ma'rifah, 1987); hardcover, 129 pp.
Review: J. Symb. Logic 54 (1989), No.4, 1494-1496
Availability: hardcopy (book)

Polchinski, Joseph

What is String Theory?
hep-th/9411028

Poletaeva, Elena

On Spencer cohomology connected with certain Lie superalgebras
Vopr. Teor. Grupp Gomologicheskoj Algebry 8 (1988), 162-167
Zentralblatt: 0677.17014 (very long of Leites)

Spencer cohomologies of Lie superalgebras of vector fields
Vopr. Teor. Grupp Gomologicheskoj Algebry 10 (1990), 168-169
Zentralblatt: 0778.17020
Description: Very short note without proofs.

Structure functions on the usual and exotic symplectic and periplectic supermanifolds
LN Phys. 375 (1991) (Differential Geom. Methods Theor. Phys., 1990), 390-395
Zentralblatt: 0744.53018
Availability: hardcopy

Integrability of the analogues of conformal and Riemannian structures on the classical superspaces
PhD Thesis, Penn State, 1992
Availability: hardcopy (in books); thesis.tar

Penrose's tensors on supergrassmanians
Math. Scand. 72 (1993), 161-190
Zentralblatt: 0791.53035
Description: Structure functions
Availability: hardcopy; Polet(Penrose).tex

Penrose's tensors. II
Math. Scand. 72 (1993), 191-211
Zentralblatt: 0791.53036
Description: structure functions
Availability: hardcopy; Polet(PenroseII).tex

Analogues of Riemann tensors for the odd metric on supermanifolds
Acta Appl. Math. 31 (1993), 137-169
Zentralblatt: 0795.53025
Description: Structure functions
Availability: hardcopy; Polet.tex

Cohomology of Lie superalgebras and string theories: problems and results
Unfinished draft, July 1996, 3pp.
Availability: cohomo-POLET.{tex,dvi,ps}; hardcopy

Semi-infinite cohomology of the loop algebra of sl(2)
CRAS 322 (1996), No.11, 1019-1023
Zentralblatt: 0904.17019
Availability: polet/

Semi-infinite cohomology and superconformal algebras
C. R. Acad. Sci. Paris 326 (1998), No.5, 533-538
Zentralblatt: 0923.17022

Semi-infinite Weil complex and N=2 superconformal algebra. I
Preprint MPI Bonn 1997-78

Semi-infinite Weil complex and superconformal algebra. II
Preprint MPI Bonn 1997-79

Contact superconformal algebras and their representations
arXiv:hep-th/0103201, 6 pages
submitted to W. Siegel et al., editors, Concise Encyclopedia of Supersymmetry, to be published by Kluwer Academic Publishers, Dordrecht, 2001
Description: 2-cocycles on K'(4).

Semi-infinite cohomology and superconformal algebras
Ann. Inst. Fourier 51 (2001), no.3, 745-768
arXiv:math.AG/0012195
Zentralblatt: pre01614235
Description: Also of current algebras.

A spinor-like representation of the contact superconformal algebra K'(4)
DOI: 10.1063/1.1326920
J. Math. Phys. 42 (2001), N1, 526-540
arXiv:hep-th/0011100
Zentralblatt: pre01711141
Description: Derivation superalgebra of C[t,t^{-1}]\otimes Lambda(2); sl(2)-subalgebras; loop sl(2)-algebra; central extensions; Witt algebra; superalgebras of pseudodifferential operators. Definition of a superconformal algebra.
Availability: k4.tar; hardcopy

Superconformal algebras and Lie superalgebras of the Hodge theory
J. Nonlin. Math. Phys. 10 (2003), no.2, 141-147
arXiv:hep-th/0209168, 7 pages
Preprint MPI Bonn 1999-136 (long version?)
Availability: sih-k1-4.{tex,dvi} (this is a much longer 34-pages version than a published paper); hardcopy (sih-k1-4.dvi)

The analogs of Riemann and Penrose tensors on supermanifolds
Preprint MPI Bonn 2003-19, 71 pp.
arXiv:math.RT/0510165
Description: Spencer cohomology of many Z-graded Lie superalgebras are computed. This is expansion of previous author's works in Yaroslavl's sborniks, LNPhys, Math. Scand.
Availability: hardcopy

On matrix realizations of the contact superconformal algebra K(4) and the exceptional N=6 superconformal algebra
Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 14 (2007), Advances in Dynamical Systems, suppl. S2, 285--289

Matrix realizations of exceptional superconformal algebras
DOI: 10.1016/j.geomphys.2008.01.005
Journal of Geometry and Physics Volume 58, Issue 6, June 2008, Pages 761-772
Description: Realizations as subalgebras of matrix algebras over the Weyl superalgebra.

Polishchuk, A. and Positselski, L.

Quadratic Algebras
AMS, 2005, 176 pp.
Description: Connection between Koszul algebras and discrete-time stichastic processes.
Availability: 21$

Pollack, R.

Restricted Lie algebras of bounded type
BAMS 74(1968), 326-331
Description: It is known from Zassenhaus, that every finite-dimensional modular Lie algebra has indecomposable representation of arbitrary large dimension. Here it is studied, whether this is true for restricted Lie algebras in the category of restricted representations. For the most (restricted) Lie algebras this is still true. For sl(2) they are more or less explicitly constructed.
Availability: hardcopy

Pollatsek, Harriet

Quantum error correction: classic group theory meets a quantum challenge
Amer. Math. Mon. 108(2001), N10, 932-
Description: A nice introduction to quantum computations.
Availability: hardcopy (journal)

Polya, G.

How to Solve It
2nd ed., Penguin Books, 1990; paperback
Availability: hardcopy (book); Kolkhoz (Russian edition)

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Mathematics and Plausible Reasonings. Vol I. Induction and Analogy in Mathematics
Princeton Univ. Press, 1954; hardcover
Availability: hardcopy (book)

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Mathematics and Plausible Reasonings. Vol II. Patterns of Plausible Inference
Princeton Univ. Press, 1954; hardcover with dustjacket
Availability: hardcopy (book)

Mathematical Discovery. Vol. II
1st corrected printing, Wiley, 1968; hardcover, 213 pp.
Availability: hardcopy (book)

Polya, G. and Szegö, G.

Aufgaben und Lehrsätze aus der Analysis, Vol. I, II
URL: http://www.mccme.ru/free-books/djvu/polya/polia-sege-1.htm http://www.mccme.ru/free-books/djvu/polya/polia-sege-2.htm http://www.krelib.com/matematika/430 http://www.krelib.com/matematika/429 http://techlibrary.ru/books.htm http://orel3.rsl.ru/mccme/djvu/polia-sege-1.djvu http://orel3.rsl.ru/mccme/djvu/polia-sege-2.djvu
4th ed., Springer, 1970, 1971; paperback
Review: Bull. Amer. Math. Soc. 84 (1978), 53-62
Availability: hardcopy (books); Kolkhoz' obmennik (Vol. 1, English edition)

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Polyak, Michael

Feynman diagrams for pedestrians and mathematicians
math.GT/0406251
Lecture notes for DennisFest, 28 pages

Polyakov, Dmitry

Teoriya superstrun
Zavtra, 2000, N8

Polyakov, L.Ya. and Semenchuk, V.N.

Characterization of the minimal non-F-groups
Russ. Math. (Izv. VUZ) 42 (1998), N4, 58-61
Description: Some generic statements about finite minimal non-F-groups, where F is a formation, and corollaries for Schmidt groups(=minimal nonnilpotent) and minimal non-supersolvable groups.
Availability: UVA

Pommaret, J.F.

Systems of Partial Differential Equations and Lie Pseudogroups
(in Russian)
Description: Including Spencer cohomology.
Availability: Kolkhoz; amazon; absent on ozon

Poncin, Norbert

Premiers espaces de la cohomologie de l'algebre de Lie graduee de Nijenhuis-Richardson de l'espace des finctions d'une variete
Bull. Belg. Math. Soc. 8(2001), 141-146
Zentralblatt: me
Availability: hardcopy

On the cohomology of the Nijenhuis-Richardson graded Lie algebra of the space of functions of a manifold
DOI: 10.1006/jabr.2001.8827
J. Alg. 243(2001), 16-40
Zentralblatt: me
Availability: hardcopy

Ponomarev, K.N. (=Ponomaryov)

Fields of representatives of commutative local rings and maximal scalar fields of finite-dimensional algebras
Algebra i Logika 37 (1998), No. 6, 667-686

Invariant Lie algebras and Lie algebras with a small centroid
DOI: 10.1023/A:1013799524982
Algebra and Logic 40 (2001), 365-377
Zentralblatt: 1033.17014
Description: Theorem. A subalgebra of a reductive (p=0) Lie algebra invariant under action of some Cartan subalgebra, has small centroid. Question: whether the same is true in positive characteristic (for, say, classical Lie algebras)?
Availability: fulltext.pdf

Automorphisms of tensor completions of algebras
DOI: 10.1007/s10469-005-0021-0
Algebra and Logic 44 (2005), N3, 205-212
Description: Automorphisms of tensor product of nonassociative algebras.
Availability: hardcopy

Ponomarev, K.N. and Firat, A.

Groups of automorphisms of Chevalley algebras
DOI: 10.1081/AGB-100105993
Comm. Alg. 29 (2001), N9, 4139-4155
Zentralblatt: 1003.17009
Abstract: An extension of Segal theorem on Lie algebra automorphisms of upper triangular nilpotent matrices to the whole class of nilpotent subalgebras generated by positive parts of indecomposable Chevalley algebras.
Availability: 100105993.pdf

Pontryagin, L.S. (=Pontrjagin)

Sur les nombres de Betti des groupes de Lie
Comptes Rendus 200 (1935), 1277-1280
Jahrbuch: 61.0475.03

Homologies in compact Lie groups
Mat. Sbornik 6 (1939), 389-422
Jahrbuch: 65.1448.03

Ueber die topologische Struktur der Lieschen Gruppen
Comment. Math. Helvetici 13 (1941), 277-283
Jahrbuch: 67.0749.02
Description: Note about priorites in computation of homology of simple Lie groups.
Availability: lie.pdf

Topological Groups
URL: http://techlibrary.ru/books.htm http://www.jstor.org/pss/3606762
Princeton Univ. Press, 5th printing, 1958; paperback, 299 pp.
3rd ed., Selected Works, Vol. 2, Gordon and Breach, 1986
Review: Math. Gazette 24 (1940), No. 259, 130-131
Availability: hardcopy (book); Kolkhoz (both English and Russian newer edition, under the title "Nepreryvnye gruppy")

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google books

Foundations of Combinatorial Topology
Graylock Press, 1952 (translation from Russian, 1947); paperback, 99 pp.
Availability: hardcopy (book)

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Gladkie mnogoobraziya i ikh primeneniya v teorii gomotopii
Nauka, 1976 (in Russian); hardcover, 176 pp.
Availability: hardcopy (book)

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Obobshcheniya chisel
2nd ed., URSS, 2003 (in Russian); paperback, 221 pp.
Availability: hardcopy (book); amazon

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Algebra
URSS, 2004 (in Russian); paperback, 134 pp.
Availability: hardcopy (book)

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Poonen, Bjorn

The moduli space of commutative algebras of finite rank
arXiv:math.AG/0608491
Journal of the European Mathematical Society Volume 10, Issue 3, 2008, pp. 817\u2013836

Pop, Iulia and Stolin, Alexander

Classification of quasi-trigonometric solutions of the classical Yang-Baxter equation
arXiv:0806.2053
Description: CYBE on the (current) Lie algebra g[t].

Pop, Ciprian

Finite sums of commutators
Proc. Amer. Math. Soc. 130(2002), 3039-3041
Abstract: Elements of unital C*-algebras without tracial states are finite sums of commutators. Moreover, the number of commutators involved is bounded, depending only on the given C*-algebra.
Description: Some references on sum of commutators in C^*-algebras.
Availability: commutators.pdf

Pop, H.

A generalization of Scheunert's theorem on cocycle twisting of Lie color algebras
arXiv:q-alg/9703002
Availability: hardcopy

Popova, N. D. and Samoilenko, Yu. S. and Strilets, O. V.

On the growth of deformations of algebras associated with Coxeter graphs
DOI: 10.1007/s11253-007-0058-4
Ukrainian Mathematical Journal Volume 59, Number 6 / June, 2007 Pages 907-918
Description: Idelogically related to examples and counterexamples to conjecture that any modular group algebra has a semisimple deformation. Braid-like relations, etc.

Popovych, R.O. and Boyko, V.M. and Nesterenko, M.O. and Lutfullin, M.W.

Realization of real low-dimensional Lie algebras
DOI: 10.1088/0305-4470/36/26/309
J. Phys. A 36 (2003), 7337-7360
arXiv:math-ph/0301029
Description: As vector fields.

Popow, A.

Identities of tensor product of two copies of Grassman algebra
Compt. Rend. Bulg. Acad. Sci. 34(1981), 1205-1208

Porkess, R.

The HarperCollins Dictionary of Statistics
HarperCollins, 1991; paperback, 267 pp.
Availability: hardcopy (book)

Poroshenko, E. N.

Grobner-Shirshov bases for the Kac-Moody algebras of the type A_n^(1)
Comm. Algebra 30 (2002), N6, 2617-2637
Availability: 120003979.pdf

Posner, E.

Differentiably simple rings
DOI: 10.2307/2034773
Proc. Am. Math. Soc. 11 (1960), 337-343
Zentralblatt: 0103.26802

Post, Gerhard

A class of graded Lie algebras of vector fields and first order differential operators
DOI: 10.1063/1.530645
J. Math. Phys. 35 (1994), 6838-6857
JMathPhys_35_6838.pdf

On the structure of transitively differential algebras
J. Lie Theory 11 (2001), No. 1, 111-128
Description: Subalgebras in Lie algebra of polynomial vector fields.
Availability: hardcopy

On the structure of graded transitive Lie algebras
J. Lie Theory 12 (2002), No.1, 265-288
Description: Subalgebras in Lie algebra of polynomial vector fields.
Availability: hardcopy

Postnikov, M.M.

Magicheskie kvadraty
Nauka, 1964
Availability: 1964-magic.djvu

Foundations of Galois Theory
Dover, 2004 (republication of Pergamon Press, 1962, translation from Russian, Fizmatgiz, 1960); paperback, 109 pp.
Availability: hardcopy (book); amazon

Lekcii po geometrii. Semestr II. Lineinaya algebra
2nd ed., Nauka, 1986 (in Russian)
Description: Interesting.
Availability: semester2-lin-alg.{pdf.djvu}; Kolkhoz

Lie Groups and Lie Algebras, Lectures in Geometry, Semester V
URSS, 1994 (translation from Russian, Nauka, 1982); hardcover, 437 pp.
Availability: hardcopy (book); Kolkhoz (Russian edition)

Potemin, G.V.

O differencialno-geometricheskikh skobkakh Poissona tretego poryadka
UMN 52(1997), N3, 173-174
Availability: UMN web site; pot05203.ps

Pourahmadi, Mohsen

DOI: 10.1093/biomet/asm073
Biometrika 94 (2007), N4, 1006-1013
Description: Seems to be estimate of covariance matrix of a very specific form (close to diagonal?). Some earlier references on estimation of covariance matrix.
Availability: 1006.pdf

Pouseele, Hannes

On the cohomology of extensions by a Heisenberg Lie algebra
Bull. Austral. Math. Soc. 71 (2005), no. 3, 459--470

Betti number behavior for nilpotent Lie algebras
DOI: 10.1007/s10711-005-9029-9
Geom. Dedicata 122 (2006), N1, 77-88
Description: An interesting survey on the behavior of cohomology of nilpotent Lie algebras, including the toral rank conjecture. Many examples. Cohomology of a Lie algebra with ideal with 1-dimensional quitient, analogous to Dixmier's result about cohomology of a Lie algebra with ideal of codimension 1.
Availability: hardcopy

Pouseele, Hannes and Tirao, Paulo

Constructing Lie algebra homology classes
J. Algebra 292(2005), N2, 585-591
Description: Of metabelian Lie algebras.

Pragacz, Piotr

A generalization of Macdonald-You formula
J. Alg. 204(1998), 573-587
Description: q-Schur functions.
Availability: macdonald.pdf

Prasad, Gopal and Rapinchuk, Andrei S.

On the existence of isotropic forms of semi-simple algebraic groups over number fields with prescribed local behavior
DOI: : 10.1016/j.aim.2006.01.001
Adv. Math. 207 (2006), N2, 646-660

Prasolov, V.V.

Problems and Theorems in Linear Algebra
AMS, 1994
Nauka-Fizmatlit, Moscow, 1996 (in Russian)
Availability: amazon; linalg.tar [table of contents and preface only]

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Polynomials
URL: ftp://ftp.mccme.ru/users/prasolov/polynoms/poly.pdf http://www.krelib.com/matematika/1300 http://www.mccme.ru/prasolov/ http://techlibrary.ru/books.htm
MCCME, 2003 (in Russain)
Springer, 2004
Availability: Kolkhoz (Russian edition); Kolkhoz' obmennik (English edition)

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Premet, Alexander A.

Toroidal Cartan subalgebras of Lie p-algebras, and anisotropic Lie algebras of positive characteristic.
Vestsi Akad. Navuk BSSR Ser. Fiz.-Mat. Navuk 1986, no.1, 9-14
MR 87j:17014
Zentralblatt: 0597.17007

Lie algebras without strong degeneration
DOI: 10.1070/SM1987v057n01ABEH003060
Mat. Sb. 129 (1986), no. 1, 140-153
MR 87g:17018
Zentralblatt: 0595.17007
Description: Every finite-dimensional Lie algebra over alg.cl. p>5, has one-dimensional inner ideal. As corollary, every such Lie algebra is either classical or with strong degeneration.
Availability: hardcopy

Inner ideals in modular Lie algebras.
Vestsi Akad. Navuk BSSR Ser. Fiz.-Mat. Navuk 1986, no.5, 11-15
MR 88d:17013
Zentralblatt: 0632.17006
Description: Results of the previous paper extended to p=5.
Availability: hardcopy

On Cartan subalgebras of Lie p-algebras
DOI: 10.1070/IM1987v029n01ABEH000964
Izv. Akad. Nauk SSSR 50 (1986), No.4, 788-800
Zentralblatt: 0613.17009
Availability: hardcopy

Absolute zero divisors in Lie algebras over a perfect field
Dokl. Akad. Nauk BSSR 31 (1987), no.10, 869-872
MR 89d:17002
Zentralblatt: 0641.17007
Description: The property to have absolute zero divisors preserved under field extension. Every simple Lie algebra is either a form of a classical Lie algebra, or has a long filtration.
Availability: hardcopy

Regular Cartan subalgebras and nilpotent elements in restricted Lie algebras
Math. USSR-Sbornik 66 (1990), no.2, 555-570
MR 90g:17017
Zentralblatt: 0698.17008
Description: Any 2 Cartan subalgebra with maximal toral part in a fin.-dim. restricted Lie alg. (alg.cl., p>0), can be obtained from each other by means of a finite chain of transformations that a similar to the exponent of the inner derivation. Corollary 3: p-operation in any restricted Lie algebra satisfies a relation of a special form.
Availability: hardcopy

Green ring of simple 3-dimensional Lie p-algebras (in Russian)
Preprint Akad. Nauk Belorus. SSR 1990, No.33, 27 pp.
Availability: hardcopy

The Green ring of the simple three-dimensional Lie p-algebra
Soviet Math. (Izv. VUZ) 35 (1991), 51-60
MR 93i:17007
Zentralblatt: 0748.17015
Availability: hardcopy

The theorem on restriction of invariants, and nilpotent elements in W_n
Math. USSR Sbornik 73 (1992), No.1, 135-159
Zentralblatt: 0737.17006
Availability: hardcopy

The Hasse principle for the groups of type E_8 over algebraic number fields
Manuscript
Description: An independent (of Chernousov) proof (with historical remarks). This essentially reduces to the proof that anisotropic forms of a Lie algebra E_8 do not exist!
Availability: Prem.hasse.{tex,dvi}

A generalization of Wilson's theorem on Cartan subalgebras of simple Lie algebras
J. Algebra 167 (1994), no.3, 641-703
MR 95f:17019
Zentralblatt: 0802.17012
Availability: hardcopy

An analogue of the Jacobson-Morozov theorem for Lie algebras of reductive groups of good characteristics
DOI: 10.2307/2154764
Trans. Amer. Math. Soc. 347 (1995), no.8, 2961-2988
MR 95k:17012
Zentralblatt: 0865.17015
Availability: 0-150.pdf

Support varieties of non-restricted modules over Lie algebras of reductive groups
JLMS 55 (1997), 236-250
Corrigenda and addednda: arXiv:0711.2128
MR 98a:17026
Zentralblatt: 0889.17019
Availability: hardcopy

Complexity of Lie algebra representations and nilpotent elements of the stabilizers of linear forms
DOI: 10.1007/PL00004612
Math. Z. 228 (1998), 255-282
MR 99i:17023
Zentralblatt: 0913.17011
Availability: hardcopy

Special traverse slices and their enveloping algebras
Adv. Math. 170 (2002), 1-55
Zentralblatt: 1005.17007
Availability: hardcopy

Nilpotent orbits in good characteristic and the Kempf-Rousseau theory
J. Alg. 260 (2003), 338-366
Availability: hardcopy

Nilpotent commuting varieties of reductive Lie algebras
arXiv:math.RT/0302204
Invent. Math. 154 (2003), N3, 653 - 683
Zentralblatt: pre02078257
Availability: hardcopy

Premet, Alexander and Semenov, K.N.

Varieties of residually finite Lie algebras.
DOI: 10.1070/SM1990v065n01ABEH001142
Math. USSR-Sbornik 65 (1990), no.1, 109-118
MR 90b:17023
Zentralblatt: 0662.17013
Description: An interesting mix of varieties and modular-Lie-algebras reasonings.
Availability: hardcopy

Premet, Alexander and Skryabin, Serge

Representations of restricted Lie algebras and families of associative $\scr L$-algebras.
J. Reine Angew. Math. 507(1999), 189-218.
MR 99m:17026
Zentralblatt: 0978.17011
Description: By using deformation arguments (in a family of associative algebras), the authors make some progress toward a proof of a Kac-Weisfeiler conjecture concerning the maximal dimension of an irreducible representation of a finitely dimensional restricted Lie algebra over an algebraically closed field of prime characteristic. The article contains an important bibliography and an interesting discussion of what is known and what is conjectured on those representations.
Availability: hardcopy

Premet, Alexander and Strade, Helmut

Simple Lie algebras of small characteristic. I. Sandwich elements
DOI: 10.1006/jabr.1996.6861
J. Algebra 189(1997), no.2, 419-480
MR 98e:17029
Zentralblatt: 0878.17019
Availability: hardcopy

Simple Lie algebras of small characteristic. II. Exceptional roots
DOI: 10.1006/jabr.1998.7746
J. Algebra 216 (1999), no.1, 190-301
MR 2000c:17034
Zentralblatt: 0939.17016
Availability: hardcopy

Simple Lie algebras of small characteristic. III. The toral rank 2 case
J. Algebra 242 (2001), no.1, 236-337
Zentralblatt: 0982.17010 0982.17010
Availability: ps3.ps; Premet's homepage

Simple Lie algebras of small characteristic. IV. Solvable and classical roots
J. Algebra 278 (2004), no. 2, 766-833
MR 2005e:17032
Zentralblatt: pre02105355

Classification of finite dimensional simple Lie algebras in prime characteristics
Contemp. Math. 413 (2006), 185-214
arXiv:math.RA/0601380
MR 2007g:17016
Zentralblatt: pre05117273
Description: Announcement of completness of classification for p>3. A survey.
Availability: hardcopy

Simple Lie algebras of small characteristic V. The non-Melikian case
J. Algebra 314 (2007), N2, 664-692
arXiv:math.RA/0601323