some bibliography: W

[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]

Wade, T.L.

Tensor algebra and Young symmetry operators
old (1950?), pp.645-657
Availability: hardcopy

Waerden, B.L. van der

Algebra
URL: http://techlibrary.ru/books.htm http://www.newlibrary.ru/book/varden_b_l_/algebra.html http://da8.boom.ru/ct/algebra.htm http://lib.prometey.org/?id=14863&page=2
Vol. I, 4th ed., Springer, 1955; hardcover
Availability: hardcopy (book); Kolkhoz (in Russian)

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Mathematische Statistik
Russian translation from Springer, 1957
Availability: vdwaerden-statistics.djvu; Kolkhoz

Wagemann, Friedrich

Some remarks on the cohomology of Krichever-Novikov algebras
DOI: 10.1023/A:1007565132203
Lett. Math. Phys. 47 (1999), N2, 173-177
Description: Krichever-Novikov algebras of Virasoro type.
Availability: L13QG314PR803430.pdf

A two-dimensional analogue of the Virasoro algebra
J. Geom. Phys. 36 (2000), 103-116
Description: H^{1,2,3} of W_1 \otime C[[t]]
Availability: wagemann.pdf

A crossed module representing the Godbillon-Vey cocycle
DOI: 10.1023/A:1007644517911
Lett. Math. Phys. 51 (2000), N4, 293-299
Description: Lie algebras of vector fields.

Explicit formulae for cocylces of holomorphic vector fields with values in \lambda densities
J. Lie Theory 11 (2001), 173-184
Zentralblatt: (me)
Availability: hardcopy

On Lie algebra crossed modules
Comm. Algebra 34 (2006), N5, 1699 - 1722
arXiv:math.KT/0611375
Description: Construction of a crossed module representing the cocycle generating H^3(L,C) for a simple complex Lie algebra.

Deformations of Lie algebras of vector fields arising from families of schemes
DOI: 10.1016/j.geomphys.2007.10.003
J. Geom. Phys. 58 (2008), N2, 165-178
Description: "Conceptual" approach to Fialowski and Schlichenmaier deformations. Sort of "infinite-dimensional" analytical deformation theory is constructed, where things can go not so well as in the classifcal deformation theory.

Wagoner, J. B.

Stability for homology of the general linear group of a local ring
DOI: 10.1016/0040-9383(76)90035-5
Topology 15 (1976), N4, 417-423

Wakimoto, Minoru

Lectures on Infinite-Dimensional Lie Algebra
World Sci., 2001, 456 pp.
Description: Representations of Kac-Moody.
Availability: 43$

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Infinite-Dimensional Lie Algebras
AMS, 2001
Availability: Kolkhoz; amazon; google books; 18$ AMS sale

Launching on a voyage into representation theory of Lie superalgebras. II
Sugaku Expositions 18 (2005), no. 2, 203--220

Walcher, Sebastian

U"ber polynomiale, insbesondere Riccatische, Differentialgleichungen mit Fundamentallo"sungen
Math. Ann. 275 (1986), 269-280
Zentralblatt: 0578.34007
Description: Subalgebras of a Lie algebra of polynomial vector fields.

On derivations of simple algebras
Algebras Groups Geom. 4 (1987), 379-382
Zentralblatt: 0643.17002
Description: A derivation D of simple nonassociative algebra over an algebraiclly closed field of char. 0 is not inner if and only if tr $D\ne 0$ and tr L(x)$=tr R(x)=0$ for all $ x\in A$. Here L(x) and R(x) denote respectively left and right translation by x.

Algebras and Differential Equations
Hadronic Press, 1991
MR 93e:34002
Zentralblatt: 0791.17002 0754.17002
Description: pp. 35-37: some generic results about idempotents and nilpotents in nonassociative algebras. Subalgebras of an algebra of polynomial vector fields.

On algebras of rank three
Comm. Algebra 27 (1999), No.7, 3401-3438
Zentralblatt: 0933.17001
Description: Commutative nonassociative algebras in which each element generates a subalgebra of dimension <= 2.

Waldhausen, Friedhelm

Algebraic K-Theory of Generalized Free Products, I, II
Ann. Math. 108(1978), No.2, 135-204,205-256
Description: Mayer-Vietoris-like exact sequence for K_0. A lot of abstract nonsense.
Availability: part[12].pdf

Waldschmidt, Michael

Diophantine Approximation on Linear Algebraic Groups: Transcendence Properties of the Exponential Function in Several Variables
Springer, 2000, 633 pp.

Walfisz, A.

Gitterpunkte in mehrdimensionalen Kugeln
Description: Representation of integers as sum of squares.
Availability: Kolkhoz

On the representation of integers by sums of squares. Asymptotic formulas
Uspekhi Mat. Nauk 7 (1952), 97-178
Amer. Math. Soc. Transl. 3 (1956), 163-248
MR 0062159
Zentralblatt: 0048.27504

Wall, C.T.C.

Graded algebras, anti-involutions, simple groups and symmetric spaces
BAMS circa 1967
Description: A sketch of a super-analog of the Brauer group.
Availability: hardcopy

A Geometric Introduction to Topology
Dover, 1993; paperback, 168 pp.
Availability: hardcopy (book)

Wall, G. E.

Lie methods in group theory
DOI: 10.1007/BFb0103128
Lecture Notes in Mathematics Volume 697/1978 (Topics in Algebra) Pages 137-173
Description: A survey.
Availability: 1978-lie.pdf

Wallace, Andrew H.

Differential Topology. First Steps
W.A.Benjamin, 1968 (Russian translation in Milnor & Wallace, Differencialnaya topologiya. Nachalnyi kurs, Platon, 1997; paperback, 277 pp.)
Availability: hardcopy (Russain translation)

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Wallace, D.A.R.

Automorphisms of groups rings
Algebra, Proc. Int. Conf. Memory A. I. Mal'cev, Novosibirsk/USSR 1989, Contemp. Math. 131, Pt. 1, 429-431 (1992)
Zentralblatt: 0763.16012
Availability: hardcopy (book)

Wallace, E.W.

Complex four dimensional Lie algebras
Proc Royal Soc. Edinburg Sec. A 65 (1958), 72-83
Zentralblatt: Zbl 0083.02105

Some remarks on anti-commutative algebras
DOI: 10.2307/2312132
Amer. Math. Mon. 69 (1962), 395-398; Correction and addendum 69 (1963), 983
Zentralblatt: 0108.03303
Description: "Bad" examples of anticommutative algebras concerning semisimplicity, solvability, radical, etc.
Availability: 1962-some.pdf; 1952-some-corr.pdf

A note on Levi's theorem
DOI: 10.2307/2315686
Amer. Math. Mon. 74 (1967), 1238
Zentralblatt: 0153.35902
Description: Example showing a failure of Levi's theorem for anticommutative algebras.
Availability: 1967-note.pdf

Two-dimensional power-associative algebras
Math. Mag. 43 (1970), 158-162
Zentralblatt: 0196.06103

Wallach, N. R.

Induced representation of Lie algebras and a theorem of Borel-Weil
Trans. AMS, 136 (1969), 181-187

Induced representations of Lie algebras. II
Proc. AMS, 21 (1969), 161-166

A class of non-standard modules for affine Lie algebras
Math. Zeit., 196 (1987), 303-313

Wallach, N. R. and Rocha-Caridi, A.

Projective modules over graded Lie algebras, I
Math. Zeit., 180 (1982), 151-172

Highest weight modules over graded Lie algebras: Resolutions, filtrations and character formulas
Trans. AMS, 277 (1983), 133-162

Characters of irreducible representations of the Lie algebra of vector fields on the circle
Invent. Math., 72 (1983), 57-76

Characters of irreducible representations of the Virasoro algebra
Math. Zeit., 185 (1984), 1-21

Wambst, Marc

Homologie de l'algèbre quantique des symboles pseudo-différentiels sur le cercle
Bull. Soc. Math. France 124(1996), 523-544
Abstract: Let [$\Psi _q$] be the quantum algebra of pseudo-differential symbols on the circle. We construct quasi-isomorphisms between the standard Hochschild complex of [$\Psi _q$] and « small » complexes. We deduce the Hochschild homology and the first cyclic homology groups of [$\Psi _q$] . These constructions give naturally rise to two cyclic 1-cocycles which turn out to be the Lie cocycles constructed by Khesin, Lyubashenko and Roger. All homology groups considered here are topological in an appropriate sense.

Homologie cyclique et homologie simpliciale aux racines de l'unité
K-Theory 23 (2001), 377-397
Description: Relates cyclic homology with "roots of unity" appearing in quantization stuff.

Wan, Zhendong

An algorithm to solve integer linear systems exactly using numerical methods
Journal of Symbolic Computation Volume 41, Issue 6 , June 2006, Pages 621-632

Wang, Yan and Cui, Ran and Deng, ShaoQiang

A class of Solvable Lie algebras
arXiv:0809.3581
Description: Solvable Lie algebras having a certain filiform Lie algebra as nilradical.

Wang, Li Yun and Meng, Dao Ji

Some results on complete Lie superalgebras
Linear Algebra and its Applications Volume 355, Issues 1-3, Pages 1-315 (1 November 2002)

Wang, Dengyin and Ou, Shikun and Yu, Qiu

Derivations of the intermediate Lie algebras between the Lie algebra of diagonal matrices and that of upper triangular matrices over a commutative ring
Lin. Multilin. Alg. 54 (2006), N5, 369 - 377

Wang, Wenkang and Puczylowski, E.R. and Li, Lian

Armendariz Rings and Matrix Rings with Simple 0-Multiplication
DOI: 10.1080/00927870701869360
Communications in Algebra, Volume 36, Issue 4 April 2008, pages 1514-1519
Availability: 794328077_content.pdf

Wang, Qing and Tan, Shaobin

First cohomology group from the Virasoro-like algebra to its Larsson functor module
DOI: 10.1080/00927870701544971
Comm. Algebra 35 (2007), N12, 4163-4174

Leibniz central extension on a Block Lie algebra
Algebra Colloq. 14 (2007), N4, 713-720

Wang, Ying and Yao, Guang-Tong

On the cohomology of associative superalgebras.
Northeast. Math. J. 17 (2001), no. 2, 175--180

Wang, Xing Tao and You, Hong

Decomposition of Lie automorphisms of upper triangular matrix algebra over commutative rings
DOI: 10.1016/j.laa.2006.05.012
Linear Algebra and its Applications Volume 419, Issues 2-3 , 1 December 2006, Pages 466-474

Wang, Dengyin (Wang, Deng-yin) and Yu, Qiu

Derivations of the parabolic subalgebras of the general linear Lie algebra over a commutative ring
DOI: 10.1016/j.laa.2006.03.010
Lin. Algebra Appl. 418 (2006), N2-3, 763-774

Derivations of the intermediate Lie algebras between the Lie algebra of diagonal matrices and that of upper triangular matrices over a commutative ring
DOI: 10.1080/03081080500412463
Lin. Multilin. Alg. 54 (2006), N5, 369-377

Wang, Dengyin (Wang, Deng-yin) and Yu, Qiu and Ou, Shi-kun

Derivations of certain Lie algebras of upper triangular matrices over commutative rings
J. Math. Res. Exposition 27 (2007), no. 3, 474--478

Wang, Dengyin and Yu, Qiu and Zhao, Yanxia

Automorphisms of a linear Lie algebra over a commutative ring
DOI: 10.1016/j.laa.2007.01.003
Lin. Alg. Appl. 423 (2007), N2-3, 324-331

Wang, Ying and Zhang, Yongzheng (=Zhang, Yong Zheng)

A new definition of restricted Lie superalgebras
Chinese Sci. Bull. 45(2000), N4, 316-321
Availability: ky0316.pdf

Derivation algebra ${\rm Der}(H)$ and central extensions of Lie superalgebras
Comm. Algebra 32 (2004), no. 10, 4117--4131
Description: General relation between skew superderivations and central extensions of a Lie superalgebra.

Wang, Weiqiang and Zhao, Lei

Representations of Lie Superalgebras in Prime Characteristic I
arXiv:0808.0046

Wang, H.

Popular Lectures on Mathematical Logic
Dover, 1993; paperback, 281 pp.
Availability: hardcopy (book)

Wang, S. P.

A note on free subgroups in linear groups
DOI: 10.1016/0021-8693(81)90117-4
J. Algebra 71 (1981), N1, 232-234
Description: In Tits alternative, the finite indices of solvable subgroups are restricted by a function dependent on n (the order of ambient linear group). This follows easily from Jordan theorem on finite solvable groups.
Availability: 1981-note.pdf; hardcopy

Wang, Shu Qin

Realizations of nontwisted affine Lie algebras over fields of prime characteristic
Pure Appl. Math. 10 (1994), no. 2, 92--100 (in Chinese)
MR 95m:17020
MR Review: The definition of an affine Lie algebra corresponding to a generalized Cartan matrix (GCM) over a field of finite characteristic has been given in two different ways: (1) by the generators and the defining relations \ref[see S. Berman, J. Algebra 27 (1973), 158--183; MR 50 #7270]; (2) by the extension of the tensor product of the Chevalley generators \ref[see H. Garland, J. Algebra 53 (1978), no. 2, 480--551; MR 80a:17012]. This paper gives the following results: (a) the equivalence of the two definitions; (b) the realization of nontwisted affine Lie algebras.

Wang, Weiqiang

Dimension of a minimal nilpotent orbit
Proc. Amer. Math. Soc. 127 (1999), 935-936.
Abstract: We show that the dimension of the minimal nilpotent coadjoint orbit for a complex simple Lie algebra is equal to twice the dual Coxeter number minus two.

Wangberg, Aaron

The structure of E6
arXiv:0711.3447
PhD Thesis, 2007, 204 pp.
Description: Some realization of the Lie algebra E_6. Structure of subalgebras.

Warhurst, Ben

Tanaka prolongation of free Lie algebras
DOI: 10.1007/s10711-007-9205-1
Geom. Dedicata 130 (2007), N1, 59-69
Description: Lie algebras for which prolongations are computed are not really free, but free nilpotent.

Wasserman, Alon

A derivation HNN construction for Lie algebras
Israel J. Math. 106 (1998), 79-92
MR 99i:17021
Description: A Lie algebra analogue to HNN extensions of groups. As a consequence, it is proved that every finite-dimensional or countable-dimensional Lie algebra A can be embedded in a Lie algebra H with two generators, and if A has a presentation with n relations, then H does also. Some algorithmic questions for finitely presented Lie algebras.
Availability: hardcopy

Waterhouse, William C.

Automorphism schemes and forms of Witt Lie algebras
J. Algebra 17 (1971), 34-40
Zentralblatt: 0212.25602

Automorphisms and twisted forms of generalized Witt Lie algebras
DOI: 10.2307/2001839
Trans. Am. Math. Soc. 327 (1991), No.1, 185-200
Zentralblatt: 0733.17007

Invariant bilinear forms on semisimple Lie algebras
Algebras Groups Geom. 9 (1992), No.1, 49-52
MR 93g:17014
Zentralblatt: 0771.17008
Abstract: All invariant bilinear forms on a semisimple Lie algebra in characteristic zero are orthogonal sums of invariants forms on the simple summands. On a simple algebra, there may be many independent ones, but they all come from the Killing form over the centroid of the algebra.
Description: Seems to be well-known (see, e.g., Bourbaki)?

Watkins, David S.

The Matrix Eigenvalue Problem. GR and Krylov Subspace Methods
Cambridge Univ. Press & SIAM, 2007

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Watson, Geoffrey S.

Spectral decomposition of the covariance matrix of a multinomial
J. Roy. Stat. Soc. Ser. B 58 (1996), No.1, 289-291
Availability: 1996-spectral.pdf

Weaver, George and Penev, Irena

From finitary to infinitary second-order logic
MLQ Volume 51, Issue 5 , Pages 499 - 506 (2005)

Wedderburn, J.H.M.

Lectures on Matrices
URL: http://www.ams.org/online_bks/coll17/ http://ef12517-2.tu-sofia.bg/Desislav Todorov/Frames/Books/Mathematics/Algebra/
AMS, 1934
Availability: Kolkhoz

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Wehrfritz, B. A. F.

2-generator conditions in linear groups
DOI: 10.1007/BF01222569
Arch. Math. 22 (1971), 237-240
Zentralblatt: 0221.20068
Availability: p2368577187l3022.pdf

Infinite Linear Groups
Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 76. Springer, 1973. xiv+229 pp
Zentralblatt: 0261.20038
Availability: hardcopy (book)

Complete reducibility in skew linear groups
DOI: 10.1112/jlms/s2-28.2.301
J. Lond. Math. Soc. 28 (1983), 301-309
Zentralblatt: 0491.20038
Availability: 301.pdf

On absolutely irreducible skew linear groups in characteristic zero
Arch. Math. 45 (1985), N3, 193 - 199
Zentralblatt: 0544.20045
Availability: x887q15248t12675.pdf

Soluble and locally soluble skew linear groups
Arch. Math. 49 (1987), N5, 379 - 388
Availability: ju2h6k4846k6lj41.pdf; hardcopy

Crossed product criteria and skew linear groups. II
Mich. Math. J. 37 (1990), No.2, 293-303
Zentralblatt: 0726.20034
Description: Results on linear hull of a skew linear group.

Crossed products, control in group algebras and absolutely irreducible groups
DOI: 10.1112/jlms/s2-42.2.209
J. Lond. Math. Soc. 42 (1990), No.2, 209-225
Zentralblatt: 0672.16010
Availability: 209.pdf

Some matrix groups over finite-dimensional division algebras
Proc. Edinb. Math. Soc., II. Ser. 33, No.1, 97-111 (1990)
Zentralblatt: 0667.20041
Description: Using Tits alternative, a similar result is proved for linear groups over division algebras.
Availability: VRII

Crossed product criteria and skew linear groups
DOI: 10.1016/0021-8693(91)90235-Z
J. Algebra 141 (1991), No.2, 321-353
Zentralblatt: 0737.16018
Availability: jalg-1991.pdf

On rings of quotients of group algebras of soluble groups of finite rank
DOI: 10.1016/0022-4049(91)90052-4
J. Pure Appl. Algebra 74 (1991), No.1, 95-107
Zentralblatt: 0763.16013
Availability: jpaa-1991.pdf

Algebras generated by locally nilpotent finitary skew linear groups
DOI: 10.1016/0022-4049(93)90031-N
J. Pure Appl. Algebra 88 (1993), No.1-3, 305-316
Zentralblatt: 0795.16016
Availability: jpaa-1993.pdf

The complete reducibility of locally completely reducible finitary linear groups
Bull. Lond. Math. Soc. 29 (1997), No.2, 173-176
Zentralblatt: 0865.20034
Availability: S002460939600159Xa.pdf

Completely reducible infinite-dimensional skew linear groups
Monatsh. Math. 129 (2000), N2, 153-157
Zentralblatt: 0956.20047
Availability: va8wx4jyy2yja8tt.pdf

Absolutely irreducible finitary skew linear groups
Q. J. Math. 51 (2000), No.2, 267-274
Zentralblatt: 0963.20028
Availability: 267.pdf

On nonmodular periodic finitary linear groups
DOI: 10.1006/jabr.1999.8054
J. Algebra 223 (2000), No.1, 295-306
Zentralblatt: 0947.20027
Availability: jalg-2000.pdf

Weibel, Chuck

History of Homological Algebra
URL: http://www.math.uiuc.edu/K-theory/0245/ http://www.math.rutgers.edu/~weibel/history.dvi
The History of Topology (ed. I.M. James), Elsevier, 1999, 797-836

An Introduction to Algebraic K-Theory

Weibel, C.A. and Geller, S.C.

Etale descent for Hochschild and cyclic homology
Preprint
Description: Behaviour of Hochschild and cyclic homology under localization.
Availability: hardcopy

Weil, Andre

Introduction à l'étude des variétés Kälériennes
Novokuzneckii Fiz.-Mat. Inst., 2000 (Russian translation from French, 1958); paperback, small format, 218 pp.
Availability: hardcopy (book); absent on amazon; Kolkhoz

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Algebras with involution and the classical groups
J. Ind. Math. Soc. 24 (1961), 589-623
Description: Classical semisimple groups over p=0, with a few exceptions, could be represented as groups of automorphisms of semisimple algebras with involution.

Osnovy teorii chisel
URL: http://eqworld.ipmnet.ru/ru/library/mathematics/numtheory.htm http://techlibrary.ru/books.htm
Mir, 1972 (Russian translation from Basic Number Theory, Springer, 1967); hardcover, 408 pp.
Availability: hardcopy (book); Kolkhoz

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Weimar-Woods, Evelyn

Contraction of Lie algebras: generalized Inonu-Wigner contractions versus graded contractions
J. Math. Phys. 36 (1995), 4519-4548

The general structure of G-graded contractions of Lie algebras. I. The classification
Canad. J. Math. 58 (2006), no. 6, 1291--1340
Availability: weimarwoods4496.pdf

The general structure of G-graded contractions of Lie algebras. II. The contracted Lie algebra
Rev. Math. Phys. 18 (2006), no. 6, 655--711

Contractions of invariants of Lie algebras with applications to classical inhomogeneous Lie algebras
DOI: 10.1063/1.2839911
J. Math. Phys. 49 (2008), 033507

Weiner, L.M.

The algebra of semi-magic squares
Amer. Math. Monthly 62 (1955), 237-239
Description: The set of all semi-magioc squares of given order form an (associative) matrix algebra. Its structure is fully determined.
Availability: 0.pdf

Weinstein, Alan

Omni-Lie Algebras
arXiv:math.RT/9912190
Description: An algebra defined as direct sum gl(V) + V with multiplication [A + v, B + w] = [A,B] + 1/2 (Aw - Bv). This 1/2 term makes the Jacobi identity to fail.

Geometric Models for Noncommutative Algebras
Description: Poisson structures, Lie algebroids, deformations.

Weinstein, F.V. (=Vainshtein, Wainstein)

Filtering bases, cohomology of infinite-dimensional Lie algebras, and Laplace operators
Funk. Anal. Pril. 19(1985), N4, 11-22
Availability: hardcopy

Cohomology of groups of braids
Seminar on Supermanifolds, Stockholm U., 1987, No. 25
Availability: hardcopy (under the same cover with Feigin)

Filtering bases: A tool to compute cohomologies of abstract subalgebras of the Witt algebra
Unconventional Lie Algebras (ed. Dmitry Fuchs), AMS, 1993
Availability: hardcopy (book); amazon

Filtering bases and cohomology of Lie algebras L(k)
math.RT/0604631

Note on Laplace operators and homologies of a few Lie subalgebras of $A_1^{(1)}$
math.RT/0604632

Weinzierl, Stefan

gTybalt - a free computer algebra system
math-ph/0304037, 22 pages
Abstract: This article documents the free computer algebra system "gTybalt". The program is build on top of other packages, among others GiNaC, TeXmacs and Root. It offers the possibility of interactive symbolic calculations within the C++ programming language. Mathematical formulae are visualized using TeX fonts.

Weisfeiler, B.

Classification of semi-simple Lie algebras over a p-adic field
Dokl. Akad. Nauk USSR 158 (1964), 258-260
Sov. Math. Dokl. 5 (1964), 1206-1208
MR 30#201
Zentralblatt: 0158.28601
Description: Also question of anisotropic algebras (in different terminology) is touched.
Availability: hardcopy

Infinite dimensional filtered Lie algebras and their connection with graded Lie algebras
Funct. Anal. Appl. 2 (1968), N1, 88-89
MR 38#1134
Description: Introduced filtration of depth > 1.
Availability: hardcopy

On the structure of the minimal ideal of some graded Lie algebras of characteristic p>0
J. Alg. 53 (1978), 344-361
Availability: hardcopy

On subalgebras of simple Lie algebras of characteristic p>0
TAMS 286 (1984), 471-503
Availability: hardcopy

Post-classification version of Jordan's theorem on finite linear groups
Proc. Nat. Acad. Sci. USA 81 (1984), no. 16, 5278-5279
MR 85j:20041
Zentralblatt: 0542.20026
Availability: hardcopy

Weisfeld, Morris

Purely inseparable extensions and higher derivations
Trans. Am. Math. Soc. 116 (1965), 435-449
Zentralblatt: 0136.32004

Tensor products of F-vector spaces
Proc. AMS 19 (1968), No.6, 1373-1378
Zentralblatt: 0181.04203
Description: Sort of filtered vector spaces with finiteness conditions and tensor products of them (looks like completed tensor product in some topology).
Availability: 0-150-1.pdf; hardcopy

Weiss, B.

Single Orbit Dynamics
AMS, 2000; paperback, 113 pp.
Availability: hardcopy (book)

Welsh, Norman

Making TeX Work
O'Reilly, 1994

Wende, Liu and Yongzheng, Zhang and Xiulinga, Wang

The derivation algebra of the Cartan-type Lie superalgebra HO
Journal of Algebra Volume 273, Issue 1 , 1 March 2004, Pages 176-205
Description: Derivations of some modular Lie superalgebra.

Wene, G. P.

The structure and classification of finite division rings
Non-associative algebra and its applications, 431--440, Lect. Notes Pure Appl. Math., 246, Chapman & Hall/CRC, 2006
Description: Should be taken with caution.

Wentworth, G.A.

Elements of Algebra
Ginn & Company, Boston, 1897; hardcover, small format, 324 pp.
Availability: hardcopy (book)

Wermuth, Nanny and Cox, D.R. and Marchetti, Giovanni M.

Covariance chains
Description: Estimation of tridiagonal covariance matrices.
Availability: hardcopy; papcovchains2.pdf; web

Wesson, Paul S

FIVE-DIMENSIONAL PHYSICS. Classical and Quantum Consequences of Kaluza-Klein Cosmology
World Sci., 2006

West, P.

Introduction to Supersymmetry and Supergravity
2nd ed., World Scientific; paperback, 425 pp.
Availability: hardcopy (book)

Westbury, Bruce W.

R-matrices and the magic square
DOI: 10.1088/0305-4470/36/7/310
J. Phys. A: Math. Gen. 36 (2003), 1947-1959; Corrigendum: 36 (2003), 2857
Abstract: The distinguished representations associated with the rows of the Freudenthal magic square have a uniform tensor product graph with edges labelled by linear functions of the dimension of the corresponding division algebra.
Availability: a30710.pdf

Sextonions and the magic square
J. London Math. Soc. 73 (2006), 455-474
arXiv:math.RA/0411428
Abstract: Associated to any complex simple Lie algebra is a non-reductive complex Lie algebra which we call the intermediate Lie algebra. We propose that these algebras can be included in both the magic square and the magic triangle to give an additional row and column. The extra row and column in the magic square corresponds to the sextonions. This is a six dimensional subalgebra of the split octonions which contains the split quaternions.

Universal characters from the MacDonald identities
DOI: 10.1016/j.aim.2005.03.013
Adv. Math. 202 (2006), N1, 50-63
Abstract: The main result of [Kostant, Invent. Math. 158 (1) (2004) 181-226, arXiv:math.GR/0309232] shows that a sequence of complexes associated with the MacDonald identities gives a sequence of universal characters which extends and generalises some representations of the exceptional series given in [Deligne, C. R. Acad. Sci. Paris Se'r. Math. 322(4) (1996) 321-326]. This proves the conjectures in [Macfarlane, Pfeiffer, J. Phys. A 36 (2003) 230 5-2317. arxiv.math-ph/0208014]. In this paper, we use a twisted version of this definition to define a sequence of complexes for the first row of the Freudenthal magic square.

Wester, Michael

A critique of the mathematical abilities of the CA Systems
in: Computer Algebra Systems: A Practical Guide (ed. M.J.Wester), Wiley, 1999
Description: an attempt of comparison of Axion, Derive, Macsyma, Maple, Mathematica, MuPAD, REDUCE as of 1996-1998.
Availability: critique.ps

Weston, Kenneth W.

An equivalence between nonassociative ring theory and the theory of a special class of groups
Proc. AMS 19(1968), No.6, 1356-1362
Description: Development on the theme of Malcev.

Westwick, Roy

Linear transformations on Grassmann spaces
Pacific J. Math. 14 (1964), 1123-1127
Zentralblatt: 0136.16402

Transformations on tensor spaces
Pacific J. Math. 23 (1967), N3, 613-620
MR 0225805
Zentralblatt: 0178.03502

Linear transformations on Grassmann spaces
Canad. J. Math. 21 (1969), 414-417
Zentralblatt: 0181.04202
Description: Linear transformations on exterior product which preserve decomposable elements.

A note on symmetry class of tensors
DOI: 10.1016/0021-8693(70)90059-1
J. Alg. 15 (1970), 309-311
Zentralblatt: 0196.05704
Description: "A symmetry class of tensors of order m of a vector space U is determined by a subgroup G of the symmetric group S_m and a character from G to the field F".

Linear transformations on Grassmann spaces. III
Linear Mult. Algebra 2 (1974), 257-268
Zentralblatt: 0297.15026

Spaces of matrices of fixed rank
DOI: 10.1080/03081088708817751
Linear and Multilinear Algebra, Volume 20, Issue 2 March 1987 , pages 171 - 174
Availability: 778401902.pdf

Transformations on tensor spaces. II
Linear Mult. Algebra 40 (1995), No.1, 81-92
Zentralblatt: 0846.15013
Description: Linear maps of tensor product of (a number) of spaces, preserving decomposable tensors, are, essentially, decomposable themselves.

Weyl, Hermann

O filosofii matematiki
Gos. Tekhniko-Teor. Izdat., Moscow-Leningrad, 1934 (in Russian)
Availability: Kolkhoz; 1934-filos.djvu

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Algebraic Theory of Numbers
Princeton Univ. Press, 1940
Availability: Kolkhoz; 1940-algebraic.djvu

The Classical Groups. Their Invariants and Representations
Gos. Izdat. Inostr. Lit., Moscow, 1947 (Russian translation from Princeton (?), 1939)
Availability: Kolkhoz; Lbs-Hbs VR II, 512.2 Wey; Lbs-Hbs Þjóðarbókhlaða, Geymsla 1, 512.2 Wey

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Philosophy of Mathematics and Natural Science
Princeton, 1949
Availability: Lbs-Hbs Þjóðarbókhlaða Geymsla 1 190.9 Wey; Abebooks.de for 11EUR

A half-century of mathematics
Amer. Math. Mon. 58 (1951), 523-553
Novoe v Zhizni, Nauke i Tekhnike, Ser. Matem. KibernetikaZnanie, Moscow, 1969
Availability: 1951-half-century.djvu (Russian translation)

Symmetry
URL: http://www.math.ru/lib/book/djvu/weyl-symmetry.djvu http://orel3.rsl.ru/nettext/12_12_05/vejl.djvu http://www.biometrica.tomsk.ru/razdel_1_1.htm
Nauka, 1968 (Russian translation from Princeton U. Press, 1952); paperback, 191 pp.
Availability: hardcopy (book); Kolkhoz

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Die Struktur der Mathematik
Usp. Mat. Nauk 31 (1976), No.4, 220-238 (in Russian)
Zentralblatt: 0333.02005
Description: Translation from appendix A to Weyl, "Philosophy of Math. and Natural Sci" (Princeton, 1949)

Izbrannye trudy. Matematika. Teoreticheskaya fizika
Nauka, 1984
Availability: Kolkhoz

Matematicheskoe myshlenie
Nauka, Moscow, 1989 (collection of Russian translations of various works); hardcover, 400 pp.
Availability: hardcopy (book); Kolkhoz

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Gesammelte Abhandlungen
4 volumes
Availability: Lbs-Hbs VR II Verkfræðibókasafn 510 Wey

Weyman, Jerzy

Resolutions of the exterior and symmetric powers of a module
J. Alg. 58(1979), 333-341
Description: A finite free resolution for modules of exterior and symmetric powers over a module M are constructed in terms of a finite free resolution of M.

Cohomology of vector bundles and syzygies
Cambridge University Press, Cambridge, 2003. xiv+371 pp.
MR 2004d:13020
Description: Theory of Schur functors and Schur complexes due to Akin-Buchsbaum-Weyman.
Availability: 0521621976WS.pdf (first 20 pages only)

Wheeler, William H.

Model theory of strictly upper triangular matrix rings
J. Symb. Log. 45, 455-463 (1980)
Zentralblatt: 0471.03027

Whitehead, G.W.

Homotopy Theory
The MIT Press, 1966; hardcover with dustjacket, 124 pp.
Availability: hardcopy (book)

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Whitehouse, Sarah

A counterexample to a conjecture of Barr
Theory Appl. Categories 2(1996), 36-39
Description: Comparison of Harrison and Andre-Quillen cohomologies.

Wiegold, James and Wilson, John S.

Growth sequences of finitely generated groups
Arch. Math. 30 (1978), 337-343
Zentralblatt: 0405.20042
Description: Growth sequence of a group G is a number of generators of G x ... x G (n times). Contrary to finite case, for infinite groups this seqeunce could be bounded. For finitely generated infinite simple group G, number of generators of G^n is less or equal then those of G + 1.
Availability: 1978-growth.pdf

Wielandt, H.

Finite permutation groups
Acad. Press (1964)

Wiener, N.

The Fourier Integral and Certain of Its Applications
Dover, 1958; paperback, 201 pp.
Availability: hardcopy (book)

Cybernetics
2nd ed., The MIT Press, 1961; hardcover, 212 pp.
Availability: hardcopy (book)

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Wigner, David

An identity in the free Lie algebra
PAMS 106(1989), N3, 639-640
Availability: hardcopy

Wigner, E.P.

Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra
Academic Press, 1959; hardcover, 372 pp.
Availability: hardcopy (book)

Wildberger, N. J.

A combinatorial construction of G_2
J. Lie Theory 13(2003), No.1, 155-165
Abstract: We show how to construct the simple exceptional Lie algebra of type G_2 by explicitly constructing its 7 dimensional representation.

A combinatorial construction for simply-laced Lie algebras
Formal power series and algebraic combinatorics (Scottsdale, AZ, 2001).
Adv. Appl. Math. 30(2003), no. 1-2, 385-396
Availability: science.pdf

Wilf, H.

generatingfunctionology
Availability: Kolkhoz

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Wilf, Herbert S. and Zeilberger, Doron

An algorithmic proof theory for hypergeometric (ordinary and "q") multisum/integral identities
Inv. Math. 108 (1992), 575-633
Description: A big interesting philosophical article, also the refs are interesting. Combinatorial identities.
Availability: idents.pdf

Wilkinson, J.H. and Reinsch, C.

Linear Algebra
Springer, 1971; hardcover, 439 pp.
Availability: hardcopy (book); absent on ozon

Willenbring, Jeb F. and Zuckerman, Gregg

Small semisimple subalgebras of semisimple Lie algebras
arXiv:math.RT/0408302
Harmonic analysis, group representations, automorphic forms and invariant theory, 403--429, Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap., 12, World Sci. Publ., Hackensack, NJ, 2007
Abstract: Let k be an sl2-subalgebra of a semisimple Lie algebra g, none of whose simple factors is of type A1. Then there exists a positive integer $b(\frak k, \frak g)$, such that for every irreducible finite dimensional $\frak g$-module $V$, there exists an injection of $\frak k$-modules $W \to V$, where $W$ is an irreducible $\frak k$-module of dimension less than $b(\frak k, \frak g)$.

Williams, Floyd L.

Laplace operators and the h module structure of certain cohomology groups
DOI: 10.2307/1996926
Trans. Amer. Math. Soc. 197 (1974), 1-57
Zentralblatt: 0353.18014
Description: H^1(n,n) and related, for a maximal nilpotent subalgebra n of a classical Lie algebra.
Availability: 1974-laplace.pdf

The cohomology of semisimple Lie algebras with coefficients in a Verma module
DOI: 10.2307/1998808
Trans. Amer. Math. Soc. 240 (1978), 115-127

Lie algebra cohomology of infinite dimensional modules
Adv. Math. 35 (1980), No. 1, 19-29
Zentralblatt: 0419.17009

Vanishing theorems for type (o,q) cohomology of locally symmetric spaces. I, II
Osaka J. Math. 18 (1981), 147-160; 2O (1983), 95-1O8

Williams, Gerald

The Tits Alternative for Groups Defined by Periodic Paired Relations
Communications in Algebra Issue: Volume 34, Number 1 / January 2006 Pages: 251 - 258

Wilson, John S. and Zelmanov, Efim I.

Identities for lie algebras of pro-p groups
DOI: 10.1016/0022-4049(92)90138-6
Journal of Pure and Applied Algebra Volume 81, Issue 1, 10 August 1992, Pages 103-109
Description: When a Lie algebra associated with a lower central series of a group is PI.
Availability: 1992-identities.pdf

Wilson, John S.

On simple pseudo-finite groups
JLMS 51 (1995), N3, 471-490
Zentralblatt: 0847.20001
Description: A group is called pseudo-finite if it is an infinite-model of the first-order theory of finite groups. There is a number k such that every element in a finite simple group is represented as a product of less than k commutators.

Finite axiomatization of finite soluble groups
DOI: 10.1112/S0024610706023106
J. London Math. Soc. 74 (2006), 566-582
Abstract: It is proved that the finite soluble groups can be characterized among finite groups by a first-order sentence, namely, the sentence that asserts that no non-trivial element $g$ is a product of 56 commutators $[x,y]$ with entries $x$, $y$ conjugate to $g$.

Wilson, R.J.

Einführung in die Graphentheorie
Vandenhoeck & Ruprecht, 1976 (German translation from Longman, 1975); paperback, 174 pp.
Availability: hardcopy ; Kokhoz (Russian edition); absent on ozon

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Wilson, Robert Lee

Classification of generalized Witt algebras over algebraically closed fields
DOI: 10.2307/1995555
Trans. Amer. Math. Soc. 153 (1971), 191-210
MR 47#5070
Description: Derivations and automorphisms of W_n(m).
Availability: 0.pdf

A characterization of p-reductive Lie algebras
DOI: 10.2307/2038313
Proc. AMS 32 (1972), No. 1, 89-90
Description: A finite-dimensional Lie p-algebra has a completely reducible faithful finite dimensional restricted representation if and only if it has no nonzero nil ideals.

A structural characterization of the simple Lie algebras of generalized Cartan type over fields of prime characteristic
DOI: 10.1016/0021-8693(76)90206-4
J. Alg. 40 (1976), 418-465
Zentralblatt: 0355.17012
Description: Filtered deformations of Lie algebras of Cartan type in a pedestrian way.
Availability: science-3.pdf

Euclidean Lie algebras are universal central extensions
DOI: 10.1007/BFb0093364
LNM 933 (1982), 210-213

Wilton, Henry

Elementarily free groups are subgroup separable
arXiv:math.GR/0511414
Proc. Lond. Math. Soc. 95 (2007), no. 2, 473--496
Description: If a group is elementary equivalent to a free goup, then every element is distinguished in a finite quotient. The proof is topological.

Winter, David J.

Representations of locally finite groups
circa 1967
Availability: hardcopy

On groups of automorphisms of Lie algebras
DOI: 10.1016/0021-8693(68)90038-0
J. Algebra 8 (1968), N2, 131-142
Availability: 1968-aut.pdf

On the toral structure of Lie p-algebras
DOI: 10.1007/BF02392385
Acta Mathematica 123 (1969), N1, 69-81

Abstract Lie Algebras
The MIT Press, 1972; hardcover with dustjacket, 150 pp.
Availability: hardcopy (book)

Cartan decomposition and Engel subalgebra triangulability
J. Alg. 62 (1980), 400-417
MR 81e:17005
Availability: hardcopy

Outer derivations and classical-Albert-Zassenhaus Lie algebras
CJM XXXVI (1984), N6, 961-972
Availability: google books; 1984-outer/ (few frist pages only)

Symmetric Lie algebras
J. Alg. 97 (1985), 130-165
Availability: hardcopy

Rootsystems of simple Lie algebras
J. Alg. 97 (1985), 166-180
Availability: hardcopy

Generalized classical Albert-Zassenhaus Lie Algebras
J. Alg. 97 (1985), 181-200
Availability: hardcopy

Reducible complements of Lie algebra radicals
Pacific J.M. 128 (1987), N1, 191-199
MR 88g:17004
Zentralblatt: 0592.17010
Description: For a modular Lie algebra L, there is a subalgebra S such that L = S + Rad(L) (not necessarily direct) and intersection of S with Rad(L) is nilpotent. Also, S can be choosen invariant under some p-powers of a fixed Cartan subalgebra.
Availability: hardcopy

The structure of cyclic Lie algebras
PAMS 100 (1987), No.2, 213-219
Zentralblatt: 0619.17011
Availability: 0-150.pdf; hardcopy

Lie algops and simple Lie algebras
DOI: 10.1081/AGB-200066145
Comm. Algebra 33 (2005), N9, 3157-3178
Description: Lie algops are pairs of associative commutative algebra and a Lie algebra acting on it. Question of classification of such simple objects is considered. Related to Lie algebras of Witt type.

Simple nil Lie algops
DOI: 10.1080/00927870601139559
Comm. Algebra 35 (2007), N4, 1093-1126

Winternitz, Pavel

Lie groups, singularities and solutions of nonlinear partial differential equations
Lecture Notes Phys. September 2003, 223-273
Abstract: It is shown how Lie group and Lie algebra theory can be used to solve partial differential equations. A method for calculating the symmetry group of a set of differential equations is presented. Special attention is devoted to algorithms for classifying subalgebras of Lie algebras. The concept of conditional symmetries is introduced and applied to perform dimensional reduction.

Subalgebras of Lie algebras. Example of sl(3,$\mathbb{R}$)
Symmetry in Physics: In Memory of Robert T. Sharp (ed. P. Winternitz et al.), AMS, 2004

Wirsching, G.J.

The Dynamical System Generated by the 3n+1 Function
LNM 1681 (1998)
Availability: printout [toc, introduction, chapter 1, bibliography only]

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Wise, Daniel T.

The rank of a direct power of a small-cancellation group
DOI: 10.1023/A:1020968914280
Geom. Dedicata 94 (2002), N1, 215-223
Description: Number of generators of a direct product of n copies of a group G. Brief history of the subject. Examples of some (infinite) group for which this number is always 2. Conjecture: for hyperbolic groups, this number is always infinity.

Wisliceny, J.

Zur Darstellung von Pro-p-Gruppen und Lieschen Algebren durch Erzeugende und Relationen
Math. Nachr. 102 (1981), 57-87
Description: A series of nilpotent Lie algebras approximating the inequality of Golod-Shafarevich-Vinberg between number of generators and relations is constructed.
Availability: hardcopy

Wit, T. de

Domain-Walls & Gauged Supergravities
Ph.D. Thesis, Univ. of Groningen, 2003; 156 pp.
Availability: hardcopy (in books)

Witherspoon, Sarah J.

Skew derivations and deformations of family of group crossed products
DOI: 10.1080/00927870600876367
math.RA/0506154
Comm. Alg. Volume 34, Number 11 / 2006 Pages: 4187 - 4206
Description: Universal deformation formulae for associative algebras arising from Hopf algebra actions.

Witt, Ernst

Treue darstellungen beliebiger liescher ringe
URL: http://www.raco.cat/index.php/CollectaneaMathematica/article/viewArticle/57278/0 http://www.imub.ub.es/collect/accdocg/COLLECTANEAMATHEMATICA_1953_06_01_03.pdf
Collectanea Mathematica 1953 Vol.: 6 Núm.: 1, 107-

Die Unterringe der freien Lieschen Ringe
MZ 64 (1956), 195-216
Description: Also for Lie p-algebras.
Availability: witt.pdf

Witte-Morris, Dave (=Morris, =Witte)

Products of similar matrices
Proc. Amer. Math. Soc. 126 (1998), 1005-1015
Description: In GL_n(K), n>2, every element is a product of elements similar to any given non-scalar element.

Real representations of semisimple Lie algebras have Q-forms
arXiv:math.RT/0205289
Algebraic groups and arithmetic, Tata Inst. Fund. Res., 2004, 469-490
Availability: hardcopy

Wodzicki, M.

Noncommutative residue. I. Fundamentals
LNM 1289(1987), 320-399 (the same "K-Theory" volume with Feigin-Tsygan)
Description: May be related with structures on H^*(L,L), though language is unclear.
Availability: UVA

Cyclic homology of differential operators
Duke M.J. 54 (1987), N2, 641-647
Availability: hardcopy; 1987-54-manin.djvu (the whole volume)

Wolf, J.A.

On the classification of Hermitian symmetric spaces
J. Math. Mech. 13 (1964), N3, 489-495
Description: Direct simple proof (earlier the classification was achieved by Cartan, Borel, Tits, and others).
Availability: CWI

Wollenberg, L.S.

Derivations of the Lie algebra of polynomials under Poisson bracket
PAMS 20(1969), 315-320

Automorphisms of the Lie algebra of polynomials under Poisson barcket
J. Math. Phys. 17(1976), 2074-2081
Zentralblatt: 0344.17009

Wolter, Kirk M.

Introduction to Variance Estimation
DOI: 10.1007/978-0-387-35099-8
2nd ed., Springer, 2007
Availability: 2007-introduction-1.pdf (1st chapter only)

Wonenburger, M.J.

Automorphisms of Cayley algebras
J. Alg. 12(1969), 441-452

Wong, Chi Song

On the use of differentials in statistics
DOI: 10.1016/0024-3795(85)90060-6
Lin. Alg. Appl. 70 (1985), 285-299
Description: A survey with examples.
Availability: 1985-use.pdf

Wong, Tsai-Lien

A note on derivations of higher order and commutativity of prime rings
Algebra Colloq. 10 (2003), no. 4, 513--517

Worz-Busekros, A.

Remarks on genetic algebras
DOI: 10.2307/1426464
Adv. Appl. Probab. 13 (1981), No. 1, 13
Availability: Worz-Busekros.pdf

Wozniakowski, H.

Numerical stability of iterations for solution of nonlinear equations and large linear systems
Preprint Dept. Comp. Sci., Carnegie-Mellon Univ., June 1975
Availability: hardcopy

Wright, Caroline B.

Second cohomology groups for algebraic groups and their Frobenius kernels
arXiv:0809.2833
Description: p=2, completing numerous earlier works.

Wright, David

The amalgamated free product structure of GL_2(k[X_1, ..., X_n])
BAMS 82(1976), 724-726
Description: Announcement of the results of the next paper.

The amalgamated free product structure of GL_2(k[X_1, ..., X_n]) and the weak Jacobian theorem for two variables
J. Pure Appl. Alg. 12(1978), 235-251
Description: Generalization (and a relatively simple proof of) Nagao's result.
Availability: science.pdf

Wu, Jie and Gerstenhaber, Murray and Stasheff, James

On the Hodge decomposition of differential graded bi-algebras
DOI: 10.1016/S0022-4049(00)00166-3
J. Pure Appl. Algebra 162 (2001), No.1, 103-125
Zentralblatt: 1059.16004
Description: Spectral sequence converging to Hochschild cohomology.

Wu, Yue Zhu (=Wu, Yuezhu) and Song, Guang Ai (=Song, Guang'ai) and Su, Yu Cai (=Su, Yucai)

Lie bialgebras of generalized Virasoro-like type
Acta Math. Sinica 22 (2006), no. 6, 1915--1922

DOI: 10.1080/00927870701247187
Lie bialgebras of generalized Witt type, II
Comm. Algebra 35 (2007), N6, 1992-2007
Zentralblatt: (me)
Availability: hardcopy

Wulfsohn, Aubrey

Tensor products of Jordan algebras
Canad. J. Math. 27 (1975), 60--74
MR 51#12952
Zentralblatt: 0276.17007
Description: Mainly counterexamples.
Availability: google books; 1975-tensor.tar

Wustner, Michael

A generalization of the Jordan decomposition
Forum Math. 15 (2003), no. 3, 395--408
Description: Related to Lie algebras

W\"uthrich, Samuel

Homology of powers of regular ideals
math.AC/0308263, 11 pages
Abstract: For a commutative ring R with an ideal I, generated by a finite regular sequence, we construct differential graded algebras which provide R-free resolutions of I^s and of R/I^s for s>0 and which generalise the Koszul resolution. We derive these from a certain multiplicative double complex. By means of a Cartan-Eilenberg spectral sequence we express Tor_*^R(R/I,R/I^s) and Tor_*^R(R/I, I^s) in terms of exact sequences and find that they are free as R/I-modules. Except for R/I, their product structure turns out to be trivial; instead, we consider an exterior product. The paper is based on ideas by Andrew Baker; it is written in view of applications to algebraic topology.

Wybourne, B.G.

Comment on "Wbase: A C package to reduce tensor products of Lie algebra representations".
Comput. Phys. Commun. - 1994. - 83, N 2-3. - 332-334

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