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Rabson, David A. and Huesman, John F. and Fisher, Benji N.
Cohomology for Anyone
Foundations of Physics 33 (12): 1769-1796, December 2003
Abstract: Crystallography has proven a rich source of ideas over several centuries. Among the many ways of looking at space groups, N. David Mermin has pioneered the Fourier-space approach. Recently, we have supplemented this approach with methods borrowed from algebraic topology. We now show what topology, which studies global properties of manifolds, has to do with crystallography. No mathematics is assumed beyond what the typical physics or crystallography student will have seen of group theory; in particular, the reader need not have any prior exposure to topology or to cohomology of groups.
Racine, M. L.
Primitive superalgebras with superinvolution
DOI: 10.1006/jabr.1997.7412
J. Algebra 206 (1998), N2, 588-614
Radu, Oana
Engel's theorem in generalized Lie algebras
M.Sc. Thesis, Memorial Univ. of Newfoundland, 2002
Radul, A.O.
The Schwarz derivative and the Bott cocycle for Lie superalgebras of string theories
Numer. Methods Diff. Eqs, Moscow, MGU, 1986, 53-67
Centralnoe rasshirenie algbery Lie differencialnykh operatotov na okruzhnosti i W-algebry
JETP Letters 50 (1989), N8, 341-343
Lie algebras of differential operators, their central extensions, and W-algebras
DOI: 10.1007/BF01090674
Functional Analysis and Its Applications Volume 25, Number 1 / January, 1991 Pages 25-39
Non-trivial central extensions of Lie algebra of differential operators in two and higher dimensions
Phys. Lett. B 265 (1991), 86-91
Raeburn, Iain and Taylor, Joseph L.
Hochschild cohomology and perturbations of Banach algebras
J. Funct. Anal. 25(1977), 258-266
Availability: hhp.pdf
Raggi-Cardenas, Alberto G. and Valero-Elizondo, Luis
Groups with isomorphic Burnside rings
Archiv der Mathematik Volume 84, Number 3 Date: March 2005 Pages: 193 - 197
Description: In many cases, a finite group is uniquely determined by its Burnside ring.
Raghunathan, M.S.
Discrete Subgroups of Lie Groups
Mir, 1977 (in Russian)
Availability: raghunathan; amazon; Euler's library
Rais, Mustapha
L'indice des produits semi-directs E x g
CRAS 287 (1978), 195-197
Notes sur l'indice des alg\`ebres de Lie (I)
arXiv:math.RT/0605499
Notes sur l'indice des alg\`ebres de Lie (II)
arXiv:math.RT/0605500
Rakhimov, I.S. and Said Husain, S.K.
On isomorphism classes and invariants of low dimensional complex filiform Leibniz algebras (part 2)
arXiv:0806.1803
Rakocevic, Miloje M.
Genetic Code: Four-Codon and Non-Four-Codon Degeneracy
arXiv:0802.1056
Description: Some numerology.
Rakviashvili, Giorgi
Cohomologies, extensions and abstract kernels of Lie p-algebras (Russian)
Soobshch Akad. Nauk Gruz. SSR (Bull. Acad. Sci.Georgian SSR) 93(1979), No. 3
Zentralblatt: 0409.17011
On the crossed enveloping algebra of Lie p-algebra (Russian)
Soobshch. Akad. Sci. Georgian SSR (Bull. Acad. Sci.Georgian SSR) 108(1982), No. 2
Zentralblatt: 0544.17007
Cohomologies of Lie p-algebras with one defining relation
Bull. Georgian Acad. Sci., 172(2005), No. 2
Ram, Arun
A survey of quantum groups: background, motivation, and results
Geometric Analysis and Lie Theory in Mathematics and Physics (ed. A. Carey and M. Murray), Australian Math. Soc. Lect. Notes Series 11, Cambridge Univ. Press, 1998, 20-104
Zentralblatt: 0901.17004
Ramabhadran, N.
Coherent pairs of extensions of Lie algebras
DOI: 10.1007/BF01110930
Math. Z. 93 (1966), N3, 189-201
Description: Extensions of the form 0 -> A -> B -> C_1 + C_2 (direct sum) -> 0. Some bicohomology is introduced.
Ramanujan, A.K.
Is there an Indian way of thinking? An informal essay
Contributions to Indian Sociology 23(1989), N1, 41-58
Description: (The author is not _the_ Ramanujan).
Availability: indian-way.pdf
Ramanujan, Srinivasa
Collected Papers of Srinivasa Ramanujan (ed. G.H.Hardy et al.)
AMS Chelsea
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Ramsey, Bobby W.
A generalization of the Lyndon-Hochschild-Serre spectral sequence for polynomial cohomology
arXiv:0712.3015
Description: Polynomial cohomology is cohomology generated by cocycles of polynomial growth.
Ran, Ziv
Lie atoms and their deformation theory
DOI: 10.1007/s00039-008-0655-x
arXiv:math.AG/0412204
Geometric And Functional Analysis Volume 18, Number 1 / April, 2008 Pages 184-221
Description: Lie atoms consists of a Lie algebra and its module, and controls data consisting of a deformation controlled by the algebra, together with a trivialization of some 'part' or 'function' of that deformation, with the trivialization controlled by the module.
Rand, D.W.
Pascal programs for identification of Lie algebras. 3. Levi decomposition and canonical basis
Comput. Phys. Commun. 46 (1987), 311-322
Rand, D. and Winternitz, P. and Zassenhaus, H.
On the identification of a Lie algebra given by its structure constants. I. Direct decopositions, Levi decompositions, and nilradicals
DOI: 10.1016/0024-3795(88)90210-8
Lin. Alg. Appl. 109 (1988), 197-246
Availability: science.pdf; hardcopy
PASCAL programs for identification of Lie algebras. Part 2: SPLIT - a program to decompose parameter-free and parameter-dependent Lie algebras into direct sums
Comp. Phys. Comm. 46 (1987), N2, 297-309
Ranicki, Andrew
Notes on ends of complexes
Talk, 1996
Availability: endnotes.pdf
Rasiowa, H. and Sikorski, R.
The Mathematics of Metamathematics
URL: http://techlibrary.ru/books.htm http://www.newlibrary.ru/book/raseva_e___sikorskii_r_/matematika_metamatematiki.html http://lib.prometey.org/?id=15291&page=4
Nauka, 1972 (Russian translation from Panstwowe Wydawnitstwo Naukowe, Warszaw, 1963); hardcover, 591 pp.
Availability: hardcopy (book); amazon; absent on ozon; Kolkhoz (Russian edition)
Rauch, G.
Effacement et deformation
Ann. Inst. Fourier 22 (1972), 239-269
Description: Description of H^3 for Lie algebras as kernels.
Availability: hardcopy
Rausch de Traubenberg, M.
Lie algebras of order F and extensions of the Poincare algebra
arXiv:hep-th/0209144
Description: Some gadgets are defined which seems to be n-ary generalizations of Lie superalgebras.
Rausch de Traubenberg, Michel and Slupinski, M. J. and Tanasa, A.
Finite-dimensional Lie subalgebras of the Weyl algebra
math.RT/0504224
J. Lie Theory 16 (2006), No. 3, 427--454
Description: Classified all finite-dimensional Lie subalgebras of the first Weyl algebra.
Ravisankar, T. S.
A note on a theorem of Jacobson
DOI: 10.2307/2036463
PAMS 21 (1969), No.3, 753-754.
Description: If A is a simple (nonassociative) algebra with identity over an algebraically closed field of char. 0, then every derivation of A is inner.
A note on a theorem of Sagle
DOI: 10.2307/2316670
Amer. Math. Monthly 76 (1969), No. 6, 652
Zentralblatt: 0176.30801
Description: Let A be a nonassociative algebra without absolute zero divisors and A^2 = A. If the Lie multiplication algebra of A is simple, then A is simple.
Availability: 1969-note.pdf
A Note on a Theorem of Kokoris
Proceedings of the American Mathematical Society, Vol. 21, No. 2 (May, 1969), pp. 355-356
Description: If A is a D-simple nonassociative algebra of the form F1 + R, then A is associative and commutative.
Availability: 2037002.pdf
On differentiably simple algebras
Pacific J. Math. 33 (1970), no. 3, 725-735
MR 0265421
Zentralblatt: 0216.07304
Description: Musing on the theme of Block's result. When differentiably-semisimple algebra is a direct sum of differentiably-simples?
Availability: 1102976838.pdf
Ray, Surajit and Lindsay, Bruce G.
Model selection in High-Dimensions: A Quadratic-risk based approach
arXiv:math/0611544
Raychaudhuri, A.K.
Classical Mechanics
Oxford Univ. Press, 1983; hardcover with dustjacket, 210 pp.
Availability: hardcopy (book)
Rayward-Smith, V.J.
A First Course in Formal Language Theory
Radio i Svyaz, Moscow, 1988 (Russian translation from Blackwell Sci. Publ., 1983), paperback, small format, 128 pp.
Availability: hardcopy
Razmyslov, Yu.P.
Finite basing of the identities of a matrix algebra of second order over a field of characteristic zero
DOI: 10.1007/BF02218641
Algebra and Logic 12 (1973), N1, 47-63
MR 49#5103
Description: Of the Lie algebra sl(2).
Availability: 1973-finite.pdf
The Jacobson radical in PI-algebras
DOI: 10.1007/BF01463354
Algebra and Logic 13 (1974), 192-204
MR 54#7536
Description: Theorem 5. If a Lie algebra L satisfies all identies of the full matrix algebra, then it has a largest solvable ideal R, and L/R is a subdirect product of semisimple finite-dimensional Lie algebras of bounded dimension.
Availability: 1974-jacobson.pdf
Algebras satisfying Capelli identities
DOI: 10.1070/IM1982v018n01ABEH001376
Math. USSR Izv. 18 (1982), 125-144
Availability: IZV_18_1_A07.pdf
Varieties of representations of finite dimensional algebras in prime algebras
Moscow Univ. Math. Bull. 13 (1982), 34-
Zentralblatt: 0522.16019
Availability: hardcopy
Finite basis property for the representations of a simple three-dimensional Lie algebra over a field of characteristic zero
Eleven Papers Translated from the Russian, AMS Transl. 140 (1988), 101-109
Algebra (Collection in Honor of the 90th Anniv. of the Birth of O.Yu. Schmidt; ed. A.I. Kostrikin), Moscow State Univ., 1982, 139-150
Zentralblatt: 0531.17007
Description: All identities of sl(2) follow from some identity of degree 5 (related to standard identity).
Availability: google print; finite.tar
Inclusions of varieties generated by simple Lie algebras
Mosc. Univ. Math. Bull. 44 (1989), No.2, 50-54
MR 90k:17064
Zentralblatt: 0707.17005
Description: p>5; Var (H_n) contained in Var A_{p^n-1}, dim H_n = dim A_{p^n-1}, but H_n and A_{p^n-1} are not isomorphic.
Availability: hardcopy
Identities of algebras and their representations
Algebra, Proc. Int. Conf. Memory A. I. Mal'cev, Novosibirsk/USSR 1989, Contemp. Math. 131, Pt. 2, 1992, 173-192
MR 93g:16035
Zentralblatt: 0773.16006
Description: A survey.
Availability: hardcopy (book)
Identities of Algebras and Their Representations
AMS, 1994 (translation from Russian, Nauka, 1989), 318 pp.
MR 95i:16022
Description: p. 30- : On isomorphism of prime algebras with the same identities.
Availability: hardcopy (book); amazon; google books
On a conjecture of Rydberg: (e/c)/(h/e) = \pi/ (in Russian)
Fundam. Prikl. Mat. 6 (2000), No.3, 873-874
MR 2001g:81283
Zentralblatt: 0982.81059
Description: Sheer madness and/or joke.
Availability: razmysl.ps
Razmyslov, Yu P and Zubrilin, K.A.
On the nilpotency of obstructions for the representability of algebras satisfying Capelli identities and representations of finite type
DOI: 10.1070/RM1993v048n06ABEH001107
Russ. Math. Surv. 48 (1993), N6, 183-184
Availability: RMS_48_6_L18.pdf
Capelli identities and representations of finite type
DOI: 10.1080/00927879408825159
Comm. Algebra 22 (1994), N14, 5733-5744
MR 95h:17025
Availability: 780147760_content.pdf
Real, Pedro
Homological perturbation theory and associativity
HHA 2(2000), N5, 51-88
Ree, Rimhak
On generalized Witt algebras.
DOI: 10.2307/1992887
Trans. Amer. Math. Soc. 83 (1956), 510-546
MR 18#491b
Zentralblatt: 0072.26203
Availability: hardcopy
The simplicity of certain nonassociative algebras
Proc. Amer. Math. Soc. 9 (1958), No. 6, 886-892
Description: Defined by means of two additive functions on abelian group.
Availability: 0.pdf
Lie elements and an algebra associated with shuffles
Ann. Math. 68 (1958), N2, 210-220
Availability: ree.pdf
Note on generalized Witt algebras
Canad. J. Math. 11 (1959), 345-352
MR 21#3468
Zentralblatt: 0088.03301
Description: Theorem: Every derivation (of generalized Witt algebra) is the sum of an inner derivation and a derivation whose matrix relative to a fixed standard basis is diagonal, provided the base field is infinite and p>2.
Availability: hardcopy
Generalized Lie elements
Can. J. Math. 12 (1960), 493-502
Zentralblatt: 0093.25503
Description: This is where color Lie algebras apparently appeared for the first time.
Availability: hardcopy
Reed, Bruce E.
Representations of solvable Lie algebras
DOI: 10.1307/mmj/1029000266
Michigan Math. J. Volume 16, Issue 3 (1969), 227-233
MR 0245630
Zentralblatt: 0204.36002
Description: A variant of Ados' theorem for solvable Lie algebras (p=0).
Reed, Mary Lynn
Algebraic structure of genetic inheritance
BAMS 34 (1997), N2, 107-130
Description: (Nonassociative) algebras arising in genetics etc.
Availability: hardcopy
Regev, Amitai
Existence of polynomial identities in A\otimes B
DOI: 10.1090/S0002-9904-1971-12871-9
BAMS 77 (1971), 1067-1069
Zentralblatt: 225.16012
Existence of identities in A \otimes B
Israel J. Math. 11 (1972), 131-152
MR 47:3442
Availability: hardcopy
Nonassociative P.I. algebras
J. Alg. 28 (1974), 247-252
Zentralblatt: 0272.17005
Description: A tensor product of a free associative algebra and a free Lie algebra does not satisfy any polynomial identity.
Availability: hardcopy
The Kronecker product of S_n-characters and an A\otimes B theorem for Capelli identities
J. Alg. 66 (1980), N2, 505-510
Young tableaux and P.I. algebras
Astérisque 87-88 (1981), 335-352
Zentralblatt: 0489.16012
Availability: Central Icelandic library, 3rd floor.
On a class of algebras defined by partitions
Adv. Appl. Math. 31 (2003), N3, 544-561
arXiv:math.CO/0210195
Description: A class of associative (super)algebras, which generalize both symmetric and exterior algberas.
Regev, Amitai and Seeman, Tamar
Z2-graded tensor products of p.i. algebras
DOI: 10.1016/j.jalgebra.2005.01.049
J. Algebra 291 (2005), N1, 274-296
Description: Z_2-graded version of Regev's theorem about tensor product of PI algebras.
Rehmann, Ulf
Central extensions of SL_2 over division rings and some metaplectic theorems
in: Contemp. Math. 55(1986)
On reflection groups and semisimple Lie algebras
Ernst Witt, Collected Papers (ed. Ina Kersten), Springer, 1998, 247-255
Description: An interesting historical survey on classification of simple Lie groups and algebras, Dynkin diagrams and all that.
Availability: spiegel.dvi
Reichstein, Zinovy
On a question of Makar-Limanov
URL: http://links.jstor.org/sici?sici=0002-9939(199601)124%3A1%3C17%3AOAQOM%3E2.0.CO%3B2-1 http://www.ams.org/proc/1996-124-01/S0002-9939-96-03014-6/home.html
Proc. Amer. Math. Soc. 124 (1996), 17-19
Zentralblatt: 0847.16015
Abstract: Let K be an uncountable field, let K \subset F be a field extension, and let A be an associative K-algebra. We show that if F \otimes_K A contains a non-commutative free algebra, then so does A.
Availability: S0002-9939-96-03014-6.ps; hardcopy
Reichstein, Zinovy and Vonessen, Nikolaus
Free subgroups of division algebras
DOI: 10.1080/00927879508825339
Comm. Algebra 23 (1995), N6, 2181-2185
Availability: 780098717.pdf
Polynomial identity rings as rings of functions
arXiv:math.RA/0407152
Description: A view on PI-rings as "close to commutatives" is exploited from the point of view of affine algebraic geometry (Zariski closed subsets etc.).
Reid, M.
Algebraicheskaya geometriya dlya vsekh
Novokuzneckii Fiz.-Mat. Inst., 1998 (Russian translation from Undergraduate Algebraic Geometry, 1988); paperback, small format, 149 pp.
Availability: hardcopy (book); google books
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Undegraduate Commutative Algebra
Cambridge Univ. Press, 1995
Availability: Kolkhoz
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Reid, G.J. and Lisle, I.G. and Boulton, A. and Wittkopf, A.D.
Algorithmic determination of commutation relations for Lie symmetry algebras of PDEs
ISSAC'92, ACM, 63-68
Availability: lie-symm.djvu
Reif, F.
Statistical Physics
Berkeley Physics Course, Vol. 5, McGraw-Hill, 1965; hardcover, 398 pp.
Availability: hardcopy (book)
Reiman, A.G.
Integrable Hamiltonian systems connected with graded Lie algebras
Zapiski Nauchn. Sem. LOMI 95(1980), 3-54
Description: Toda chains
Availability: hardcopy; 1980-95.djvu (whole journal issue)
Reiman, A.G. and Semenov-Tyan-Shanskii, M.A.
Current algebras and nonlinear partial differential equations
Soviet Math. Dokl. 21(1980), N2, 630-
Availability: hardcopy
Teoretiko-gruppovye metody v teorii konechnomernykh integriruemykh sistem (in Russian)
Dinamicheskie Sistemy - 7, VINITI, 1987, 119-194
Availability: hardcopy (scan, in books); dynsyst-7.djvu (whole book)
Soglasovannye skobki Poissona dlya Laksovykh uravnenooi i klassicheskie r-matricy
Zapiski Nauchn. Sem. LOMI 164(1987),
Description: Agreed Possion brackets, i.e. those whose sum is again a Poisson bracket.
Availability: 1987-164.djvu (whole journal issue)
Reiner, David L.
Enumeration in music theory
Amer. Math. Monthly 92(1985), N1, 51-
Availability: enumeration.pdf
Reiner, Victor and Webb, Peter
DOI: 10.1016/j.jpaa.2003.12.006
J. Pure Appl. Algebra 190 (2004), N1-3, 291-327
Abstract: We study a combinatorially defined double complex structure on the ordered chains of any simplicial complex. Its columns are related to the cell complex Kn whose face poset is isomorphic to the subword ordering on words without repetition from an alphabet of size n. This complex is shellable and as an application we give a representation theoretic interpretation for derangement numbers and a related symmetric function considered by De'sarme'nien and Wachs [11]. We analyze the two spectral sequences arising from the double complex in the case of the bar resolution for a group. This spectral sequence converges to the cohomology of the group and provides a method for computing group cohomology in terms of the cohomology of subgroups. Its behavior is influenced by the complex of oriented chains of the simplicial complex of finite subsets of the group, and we examine the Ext class of this complex.
Availability: science.pdf
Reiterman, Jan
One more categorical model of universal algebra.
MR 58#16464
Description: "... a new categorical definition of an equational variety of algebras over a general category and validity of a Birkhoff type theorem. Approach is to use a free algebra construction which simulates inductive forming of words over variables..."
The Birkhoff theorem for finite algebras
Algebra Universalis 14 (1982), no.1, 1-10
MR 84c:08008
Zentralblatt: 0484.08007
Abstract: A finite analogue of the Birkhoff variety theorem is proved: A nonvoid class of finite algebras of a finite type $\tau$ is closed under the formation of finite products, subalgebras and homomorphic images if and only if it is definable by equations for implicit operations... (=pseudoequations)
Remeslennikov, V.N.
\exists-free groups
Sibirsk. Mat. Zh. 30 (1989), N6, 193-197
Availability: hardcopy; remeslennikov.pdf
\exists-Free groups as groups with length function
DOI: 10.1007/BF01056955
Ukrainian Math. J. 44 (1992), N6, 733-738
Availability: hardcopy; 1992-exists-free.pdf
\exists-free groups and groups with length function
Contemp Math. 184 (1995), 369-376
Description: A clear and interesting survey of preceding two papers.
Availability: hardcopy (book)
Remeslennikov, V. N. and Roman'kov, V. A.
Model-theoretic and algorithmic questions in group theory
DOI: 10.1007/BF02106805
J. Math. Sci. 31 (1985), N3, 2887-2939
Alg. Top. Geom., Vol. 21, VINITI, 1983, 3-
Description: A VINITI survey.
Availability: x70826501r77qh10.pdf
Remeslennikov, Vladimir and Stohr, Ralf
The equation [x,u] + [y,v] = 0 in free Lie algebras
DOI: 10.1142/S0218196707004104
Intern. J. Algebra Comput. 17 (2007), N5/6, 1165-1187
Remm, Elisabeth
Affine structures on nilpotent contact Lie algebras
math.RA/0109077
Description: Affine structure on a Lie algebra L is a bilinear map d:L x L -> L satisfying d(x,y) - d(y,x) = [x,y]; d(x,d(y,z)) - d(y,d(x,z)) = d([x,y],z).
Operades Lie-admissibles
DOI: 10.1016/S1631-073X(02)02408-1
C. R. Math. Acad. Sci. Paris 334 (2002), no. 12, 1047-1050
math.RA/0210324
Description: Classes of Lie-admissible algebras containing the associative algebras, the Vinberg algebras and pre-Lie algebras.
Repin, D. V.
Graded identities of a simple three-dimensional Lie algebra
Vestn. Samar. Gos. Univ. Estestvennonauchn. Ser. 2004, Special Issue 2, 5--16 (in Russian)
MR 2006a:17001
Availability: 200460001.pdf
Reshetnikov, V.N.
O kogomologiyakh dvukh beskonechnomernykh algebr Lie
Izv. VUZ 1971, N5, 74-81; Corrigenda: some later issue (?), p.101
Availability: hardcopy
Cohomologii algebry Lie vektornykh polei na mnogoobrazii, obrashchayushchikhsya v nul v dannoi tochke
UMN 1 (1972), N1, 251-252
Availability: CWI
Retakh, Vladimir S.
Massey operations in Lie superalgebras and deformations of complex-analytic algebras
Funkts. Anal. Prilozh. 11 (1977), No.4, 88-89
Funct. Anal. Appl. 11 (1978), 319-321
Zentralblatt: 0389.17005
Description: (Seemingly) "high-order" Massey brackets arising from the standard cohomological settings are defined.
Operations de Massey, la construction S et extensions de Yoneda
CRAS 299 (1984), N11, 475-478
Description: Glueing together short exact sequences in various categories. Largely abstract nonsense.
Availability: hardcopy
Lie-Massey brackets and n-homotopically multiplicative maps of differential graded Lie algebras
J. Pure Appl. Algebra 89 (1993), No.1-2, 217-229
Zentralblatt: 0781.17013
Description: "High-order" Massey brackets arising from the standard cohomological...
Availability: retakh.pdf
Retakh, V. S. and Feigin, B.L.
Cohomology of some Lie algebras and superalgebras of vector fields
Uspekhi Mat. Nauk 37 (1982), no. 2(224), 233--234.
Russian Math. Surveys 37 (1982), no. 2, 251--252
MR 83m:58083
Zentralblatt: 0505.58040
Reutenauer, Christophe
Se'ries formelles et alge`bres syntactiques
DOI: 10.1016/0021-8693(80)90097-6
J. Algebra 66 (1980), N2, 448-483
Description: To each formal power series one associates a syntactique algebra.
Free Lie Algebras
London Math. Soc. Monographs, N7, Oxford Univ. Press, 1993, 269pp.
MR 94j:17002
Availability: 1993-free.djvu; Kolkhoz' obmennik
Free Lie Algebras
Preprint IRMA, 2001, 013
Handbook of algebra, Vol. 3, 887--903, North-Holland, 2003
Description: Survey of different bases in and standard facts on free Lie algebras
Availability: 01013.ps ; vol3.djvu (whole book)
Revesz, G.
On a construction of the universal field of fractions of a free algebra
Mathematika 31, 227-233 (1984)
Zentralblatt: 0573.16010
Description: Embedding-into-ultrapower theme.
Revoy, Philippe
Algèbres de clifford et algèbres extérieares
DOI: 10.1016/0021-8693(77)90404-5
Journal of Algebra Volume 46, Issue 1 , May 1977, Pages 268-277
Description: In the context of filtered and associated graded algebras.
Availability: 1977-algebres.pdf
Alge`bres de Lie quadratiques non re'solubles
Pre'publication U.Montpellier 98-23
Description: Quadratic Lie algebra is a Lie algebra equipped with bilinear symmetric invariant nondegenerate form.
Revyakin, A.M.
Matroids
J. Math. Sci. 108(2002), N1, 71- (English)
Itogi Nauki i Tekhniki, Computing Mathematcis and Cybernetics - 3, VINITI, 2002 (Russian)
Description: A survey.
Availability: fulltext.pdf
Reyman, A.G. and Semenov-Tian-Shansky, M.A.
Integriruemye sistemy
URL: http://www.krelib.com/matematika/4232 http://techlibrary.ru/books.htm
Inst. Comput. Issled., Moscow-Izhevsk, 2003 (in Russian); 351 pp.
Availability: hardcopy (book)
Rezaei-Aghdam, A. and Hemmati, M. and Rastkar, A.R.
Classification of real three-dimensional Lie bialgebras and their Poisson-Lie groups
DOI: 10.1088/0305-4470/38/18/008
arXiv:math-ph/0412092
J. Phys. A 38 (2005), no. 18, 3981--3994
Rice, J.A.
Mathematical Statistics and Data Analysis
2nd ed., China Machine Press (reprint of Wadsworth Inc, 1995); paperback, 602 + 49 pp.
Availability: hardcopy (book)
Richard, Lionel
Homologie et cohomologie de Hochschild de certaines algebres polynomiales classiques et quantiques
arXiv:math.QA/0207073, 41pp.
Abstract: We study Hochschild homology and cohomology for some polynomial algebras mixing both ``classical'' relations (XY-YX=1) and ``quantum'' relations (XY=lYX). More specifically, we prove that the algebra of differential operators on any quantum affine space (quantum Weyl algebra) have the same Hochschild homology, and satisfy the same duality relation, as the classical Weyl algebra does.
Richard, Lionel and Silvestrov, Sergei D.
Quasi-Lie structure of sigma-derivations of C[t^{+-}]
DOI: 10.1016/j.jalgebra.2007.09.029
J. Algebra Volume 319, Issue 3, 1 February 2008, Pages 1285-1304
Richardson, A. R.
Simultaneous Linear Equations over a Division Algebra
DOI: 10.1112/plms/s2-28.1.395
Proc. London Math. Soc. 1928 s2-28: 395-420
Availability: 395.pdf
Richardson, J.M.
Pattern recognition and group theory
Frontiers of pattern (Watanabe S., ed.), Academic Press, 1972, 453-477
Description: A survey
Availability: tcsi-4.djvu
Richardson, R.W.
A rigidity thorem for subalgebras of Lie and associative algebras
Illinois J.M. 11(1967), 92-110
Availability: CWI
On the rigidity of semi-direct products of Lie algebras
Pacific J.M. 22(1967), N2, 339-344
Conjugacy classes in Lie algebras and algebraic groups
Ann. Math. 86(1967), No.1, 1-15.
Availability: 0-150.pdf
Commuting varieties of semisimple Lie algebras and algebraic groups
Compos. Math. 38(1979), 311-327
Description: In any reductive Lie algebra, the commuting variety {(x,y)|[x,y]=0} is approxiamted by a pair of elements belonging to a Cartan subalgebra. Over any algebraically closed field, approximation may be understood in a sense of Zarisky topology, and over R and C - in the usual (Hausdorff) topology.
Availability: hardcopy
Richter, Birgit
The collapse of the periodicity sequence in the stable range
arXiv:math.KT/0601326
Description: A survey of different cohomologies for commutative algebras. For certain Gamma homology (which coincides with Andre-Quillen homology for Q-algebras) a cyclic variant is introduced.
Richter, M.M.
Some aspects of nonstandard methods in general algebra
Universal algebra and its links with logic, algebra, combinatorics and computer science, Proc. '25. Arbeitstag. Allgemeine Algebra', Darmstadt 1983, Res. Expo. Math. 4, 78-84 (1984)
Zentralblatt: 0551.03038
Riedel, Herbert H. J.
Growth sequences of finite algebras
DOI: 10.1007/BF01236808
Algebra Universalis 20 (1985), 90-95
Description: For every finite universal algebra A, the number of generators of A x ... x A (n times) tends to infinity as n tends to infinity. Earlier this was proved by Wiegold for finite groups.
Righi, Celine
Enumeration of ad-nilpotent ideals of parabolic subalgebras for exceptional types
arXiv:0804.2404
Description: Using GAP.
Riguet, Jacques
Calcul differential libre
Sem. Bourbaki, December 1954, Exp. 105
Description: Fox calculus.
Availability: hardcopy
Riley, David M.
The tensor product of Lie soluble algebras
DOI: 10.1007/BF01781555
Arch. Math. 66 (1996), N5, 372-377
Description: Tensor product of Lie nilpotent or metabelian associative algebras is Lie soluble.
Availability: 1996-tensor.pdf
PI-Algebras generated by nilpotent elements of bounded index
DOI: 10.1006/jabr.1996.6940
J. Algebra 192 (1997), N1, 1-13
Description: Associative PI-algebras generated by nilpotent elements, and from non-matrix varieties, are nil.
How abelian is a finite-dimensional Lie algebra?
Forum Math. 15 (2003), no.3, 455-463
Description: Roughly, all Lie algebras of large finite dimension contain abelian subalgebras of large finite dimension (p=0 or p>5, alg. cl.). For p>0, the proof is based on Premet's theorem on Lie algebras without strong degeneration.
Availability: forumabelian.{dvi,pdf}
Riley, D. M. and Shalev, A.
The Lie structure of enveloping algebras
DOI: 10.1006/jabr.1993.1240
J. Algebra 162(1993), N1, 46-61
Description: When a restricted universal envelope is Lie-soluble or nilpotent?
Riley, David M. and Tasic, Vladimir
The transfer of a commutator law from a nil-ring to its adjoint group
Canad. Math. Bull. 40 (1997), 103-107
Description: Tensor product of two Lie-nilpotent associative algebras.
Riley, David and Usefi, Hamid
The isomorphism problem for universal enveloping algebras of Lie algebras
Algebr. Represent. Theory 10 (2007), no. 6, 517--532
Riley, D.M. and Wilson, Mark
Group algebras and enveloping algebras with nonmatrix and semigroup identities
Comm. Alg. 27 (1999), 3545-3556
MR 2000c:16032.
Abstract: Let $K$ be a field of characteristic $p>0$. Denote by $\omega(R)$ the augmentation ideal of either a group algebra $R=K[G]$ or a restricted enveloping algebra $R=u(L)$ over $K$. We first characterize those $R$ for which $\omega(R)$ satisfies a polynomial identity not satisfied by the algebra of all $2\times 2$ matrices over $K$. Then, we examine those $R$ for which $\omega(R)$ satisfies a semigroup identity (that is, a polynomial identity which can be written as the difference of two monomials).
Rim, D.S.
Deformations of transitive Lie algebras
DOI: 10.2307/1970435
Ann. Math. 83 (1966), 339-357
Description: Filtered deformation of transitive Lie algebras described by Spencer cohomology.
Availability: 0.pdf; hardcopy
Rinehart, G.
Differential forms on general commutative algebras
DOI: 10.2307/1993603
TAMS 108(1963), 195-222
Description: Cohomology of Lie-Rinehart algebras.
Availability: 0.pdf
Ringel, Claus Michael
Hall algebras and quantum groups.
Inv. Math. 101 (1990), 583-591
Description: A construction corresponding to a category of modules certain associative algebra whose relations are goverened by module extensions.
The development of the representation theory of finite-dimensional algebras. 1968-1975
Representation Theory and Algebraic Geometry, 1997, 89- , Cambridge Univ. Press
Availability: Google books; 89.png (first page only)
Ringwood, G.A.
The structure of Poisson algebras
DOI: 10.1093/imammb/2.1.69
Mathematical Medicine and Biology 2 (1985), N1, 69-73
Description: Filtration on some class of algebras is emphasized.
Availability: 69.pdf; hardcopy
Riordan, John
An Introduction to Combinatorial Analysis
Izdat. Inostr. Lit., Moscow, 1963 (Russian translation from John Wiley & Sons, 1958)
Availability: Kolkhoz
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Combinatorial Identities
Nauka, 1982 (Russian translation from Wiley, 1965)
Availability: absent on amazon; Kolkhoz
Ritt, J.F.
URL: http://www.ams.org/online_bks/coll33/ http://ef12517-2.tu-sofia.bg/Desislav Todorov/Frames/Books/Mathematics/Differential Algebra/
Differential Algebra, AMS
Availability: amazon; Kolkhoz
Rittenberg, V. and Wyler, D.
Sequences of Z_2 + Z_2 graded Lie algebras and superalgebras
J. Math. Phys. 19(1978), 2193-2200
Zentralblatt: 0423.17004
Description: It seems here the term "color Lie algebras" was introduced.
Availability: JMP02193.pdf
Generalized superalgebras
Nuclear Physics B 139(1978), N3, 189-202
Description: Z_n + Z_n- and Z_2 + ... + Z_2-graded color algebras.
Availability: science.pdf
Ritter, William Gordon
Geometric quantization
arXiv:math-ph/0208008, 6pp.
Abstract: We attempt to give the shortest possible self-contained introduction to the main idea of geometric quantization. Some familiarity with symplectic geometry and quantum mechanics is assumed.
Quantum field theory and the space of all Lie algebras
arXiv:math-ph/0304031, 10 pages
Abstract: The space $\M_n$ of all isomorphism classes of $n$-dimensional {Lie} algebras over a field $k$ has a natural non-Hausdorff topology, induced from the Segal topology by the action of $\GL(n)$. One way of studying this complicated space is by topological invariants. In this article we propose a new class of invariants coming from quantum field theory, valid in any dimension, inspired by Jaffe's study of generalizations of the Witten index.
Rivin, I. and Vardi, I. and Zimmermann, P.
The n-queens problem
DOI: 10.2307/2974691
Amer. Math. Monthly, 101 (1994), 629-639.
Availability: nqueens.pdf
Roberts, Justin
Unusual formulae for the Euler characteristic
J. Knot Theory Ramif.
arXiv:math.GT/0201178
Abstract: Everyone knows that the Euler characteristic of a combinatorial manifold is given by the alternating sum of its numbers of simplices. It is shown that there are other linear combinations of the numbers of simplices which are combinatorial invariants, but that all such invariants are multiples of the Euler characteristic.
Robins, Vanessa
Towards computing homology from finite approximation
Manuscript, 2000
Availability: hardcopy; web
Computational topology for point data: Betti numbers of alpha-shapes
Lect. Notes Phys. 600 (2002), 261-274
Availability: web; hardcopy
Robins, V. and Abernethy, J. and Rooney, N. and Bradley, E.
Topology and intelligent data analysis
DOI: 10.1007/b13240
Lect. Notes Comp. Sci. 2810 (2003), Adv. Intelligent Data Analysis V, 111-122
Description: A short survey of other articles of Robins (et al.).
Availability: hardcopy; ida03.ps
Robins, V. and Meiss, J. D. and Bradley, E.
Computing connectedness: disconnectedness and discreteness
DOI: 10.1016/S0167-2789(99)00228-6
Physica D: Nonlinear Phenomena 139 (2000), N3-4, 276-300
Availability: hardcopy
Robinson, Alan and Whitehouse, Sarah
Operads and Gamma-homology of commutative rings
Math. Proc. Cambridge Phil. Soc. 132(2002), 197-234
Description: Cohomology for commutative rings is defined which is "very different" from Andre-Quillen cohomology.
Robinson, A.
A note on embedding problems
Fundamenta Math. 50 (1962), 455-461
Description: Probably the "Robinson-Amitsur ultrafilter".
Introduction to Model Theory and to The Metamathematics of Algebra
Nauka, 1967 (Russian translation from North-Holland, 1963); hardcover, 376 pp.
Availability: hardcopy (book); amazon; absent on ozon; Kolkhoz (Russian edition)
Robinson, D.J.S.
Finitness conditions and generalized soluble groups. I
Springer, 1972
Description: Infinite groups all whose proper subgroups are finite.
Robinson, Sara
Computer scientists find unexpected depths in airfare search problem
URL: http://www.itasoftware.com/news/pr/siam.php http://www.siam.org/news/news.php?id=456
SIAM News 35(2002), N6, July-August
Description: The problem to find the best airfare price is NP-hard.
Rodriguez, Miguel A. and Winternitz, Pavel
Lie symmetries and exact solutions of first order difference schemes
nlin.SI/0402047
J. Phys. A: Math. Gen. 37(2004), 6129-6142
Abstract: We show that any first order ordinary differential equation with a known Lie point symmetry group can be discretized into a difference scheme with the same symmetry group. In general, the lattices are not regular ones, but must be adapted to the symmetries considered. The invariant difference schemes can be so chosen that their solutions coincide exactly with those of the original differential equation.
Roganov, Yu.V.
Rigidity of minimal algebras
Math. USSR Sbornik 24(1974), N4, 482-486
Description: Let I be partially ordered set, and A is an associative algebra with a basis e_ij, i,j in I, e_ij e_pq = \delta_jp e_iq. Then H^2(A,A) = 0.
Availability: VU
Roger, C.
Cohomology of current Lie algebras
Deformation Theory of Algebras and Structures and Applications, 1988, 357-374
Zentralblatt: 0663.17008
Description: A survey; ref. to Feigin's and Loday-Quillen results; deformations of current algebras.
Availability: hardcopy
Description: Chapters from apparently unpublished book. Chap. 4 deals with cohomology of Virasoro algebra and Chap. 9 deals with supermathematics.
Availability: roger-book.tar
Roger, C. and Elgaliou, M. and Tihami, A.
Une cohomologie pour les algèbres de Lie de Poisson homogènes.
Publ. Dép. Math., Nouv. Sér., Univ. Claude Bernard, Lyon 1990, 1-26
MR 95j:58183
Zentralblatt: 0841.58027
Roger, Claude and Vanhaecke, Pol
Poisson cohomology of the affine plane
J. Algebra 251 (2002), no.1, 448-460
Description: Poisson cohomology and deformations of Poisson algebras.
Availability: second author's web site
Rogers, Alice
Supermanifolds: Theory and Applications
World Sci., 2007
Roggenkamp, K.W.
Isomorphism problem for finite group rings
Contemp. Math. 184 (1995), 285-
Availability: hardcopy (book)
Rohn, Jiri
Nonsingularity, positive definiteness, and positive invertibility under fixed-point data rounding
Appl. Math. 52 (2007), no. 2, 105--115
Rohr, Rudolf Philippe
Lie algebras generated by 3-forms
DOI: 10.1016/j.crma.2006.01.006
Comptes Rendus 342 (2006), N6, 381-385
Availability: sdarticle.pdf
Rohrl, Helmut (=Roehrl)
A categorical setting for determinants and traces
Nagoya Math. J. 34 (1969), 35-76
MR 0242929
Zentralblatt: 0176.28801
A theorem on non-associative algebras and its application to differential equations
DOI: 10.1007/BF01168018
Manuscripta Math. 21 (1977), no. 2, 181--187
Zentralblatt: 0358.17004
Description: Over algebraically closed field. The number of pairwise linearly independent idempotents and nilpotents is either infinite, or else positive and no more than 2^n - 1. In the former (infinite) case, a nilpotent of index 2 exists.
On the zeros of polynomials over arbitrary finite dimensional algebras
DOI: 10.1007/BF01168049
Manuscr. Math. 25 (1978), 359-390
Zentralblatt: 0425.17001
Availability: fulltext.pdf
Finite dimensional algebras without nilpotents over algebraically closed fields
DOI: 10.1007/BF01238461
Arch. Math. 32 (1979), 10-12
Zentralblatt: 0387.17001
Availability: 1979-finite.pdf
Ro"hrl, Helmut and Walcher, Sebastian
Some classes of algebras and their derivation algebras
Algebras Groups Geom. 4 (1987), No.4, 475-496
Zentralblatt: 0669.17006
Description: When the dimension of a derivation algebra of a finite-dimensional nonassociative algebra is maximal possible?
Algebras of complexity one
Algebras Groups Geom. 5 (1988), No.1, 61-107
Zentralblatt: 0659.17002
Description: Complexity = dimension - number of generators. Derivations of such algebras.
Ro"hrl, Helmut and Wischnewsky, Manfred Bernd
Subalgebras that are cyclic as submodules
Manuscr. Math. 19 (1976), 195-209
Zentralblatt: 0333.17002
Description: When a finite-diemensional nonassociative algebra contains either nilpotent or idempotent? Over an algebraically closed field or reals - always.
Roitman, Michael
Combinatorics of free vertex algebras
arXiv:math.QA/0103173
Description: Vertex algebras given by generators and relations, free vertex algebras.
Invariant bilinear forms on a vertex algebra
DOI: 10.1016/j.jpaa.2004.05.005
J. Pure Appl. Alg. 194 (2004), N3, 329-345
arXiv:math.QA/0210432
Description: Seems to be a more general (an more "algebraic") definition of vertex algebra than usual.
Rollenske, Sönke
Nilmanifolds: complex structures, geometry and deformations
PhD Dissertation, Universität Bayreuth, 2007
Description: Lie algebras with complex structure, some associated cohomology.
Romagny, Matthieu
Determinants of finite-dimensional algebras
arXiv:0712.1892
Description: Prop. 5.3.2: Irreducible components (in the algebraic variety of all n-dimensional algebras) of semisimple associative algebras.
Romalis, G.M.
Gruppy s invariantnymi podgruppami konechnogo indeksa (in Russian)
Mat. Zapiski Uralsk. Gos. Univ. 9(1974), N1, 105-109
Availability: hardcopy
Romalis, G. M. and Sesekin, N. F.
O metagamiltonovykh gruppakh
Mat. Zapiski Uralsk. Gos. Univ. 5 (1966), tetrad' 3, 101-106
MR 34#2696
Description: Groups in which all non-abelian subgroups are normal.
Availability: absent in Iceland, VU, UVA and CWI
O metagamiltonovykh gruppakh,
Mat. Zapiski Uralsk. Gos. Univ. 6 (1968), 50-52
Availability: absent in Iceland, VU, UVA and CWI
Romeijn, Jan-Willem and Schoot, R. van de
A Philosophical Foundation of Null, Alternative and Informative Hypotheses
Null, Alternative and Informative Hypotheses, Hoijtink, Klugkist and Boelen (eds.), to appear
Romero, A. and Rubio, J. and Sergeraert, F.
Computing spectral sequences
cs.SC/0602064
Journal of Symbolic Computation Volume 41, Issue 10 , October 2006, Pages 1059-1079
Description: Lisp, algebraic topology.
Rose, Bruce I.
Model theory of alternative rings
DOI: 10.1305/ndjfl/1093888315
Notre Dame J. Formal Logic 19 (1978), no. 2, 215-243
MR 0485338
Zentralblatt: 0351.02037
Availability: 1093888315.pdf
The \aleph_1-categoricity of strictly upper triangular matrix rings over algebraically closed fields
J. Symb. Log. 43 (1978), 250-259
Zentralblatt: 0385.03026
Rings which admit elimination of quantifiers
DOI: 10.2307/2271952
J. Symb. Log. 43 (1978), 92-112; Corrigendum: 44 (1979), 109-110
Zentralblatt: 0388.03010, 0398.03013
On the model theory of finite-dimensional algebras
DOI: 10.1112/plms/s3-40.1.21
PLMS 40 (1980), N1, 21-39
Zentralblatt: 0463.03020
Description: Algebras are considered as models in the ring signature, without predicates specifying the underlying field.
Availability: 21.pdf
Prime quantifier eliminable rings
DOI: 10.1112/jlms/s2-21.2.257
J. Lond. Math. Soc. 21 (1980), 257-262
Zentralblatt: 0439.03011
Preservation of elementary equivalance under scalar extension
DOI: 10.2307/2273095
J. Symb. Logic 47 (1982), N4, 734-738
Zentralblatt: 0514.03018
Description: Of algebras.
Availability: rose.pdf; hardcopy
Rosebrugh, R. and Wood, R.J.
Relational databases and indexed categories.
CMS Conf. Proc., V.13, "Category Theory 1991: Proceedings of the 1991 Summer
Category Theory Meeting, Montreal, Canada", 1992
Rosellen, Markus
A Course in Vertex Algebra
arXiv:math/0607270, 204 pp.
Rosen, Robert
The DNA-protein coding problem
DOI: 10.1007/BF02476459
Bull. Math. Biophysics 21 (1959), N1, 71-95
Description: Free semigroups. Biological significance of freness?!
Availability: 1959-dna.pdf
Some further comments on the DNA-protein coding problem
DOI: 10.1007/BF02477917
Bull. Math. Biophysics 21 (1959), N3, 289-297
Availability: 1959-some.pdf
Some further comments on the DNA-protein coding problem: A correction and a note
DOI: 10.1007/BF02478006
Bull. Math. Biophysics 22 (1960), N2, 199-205
Availability: 1960-some.pdf
Rosenbaum, M and Vergara, J D
The Hopf algebra of renormalization, normal coordinates and Kontsevich deformation quantization
J. Phys. A: Math. Gen. 37(2004), 7939-7953
Availability: a4_32_008.pdf
Rosenberg, Alex and Zelinsky, Daniel
Cohomology of infinite algebras
DOI: 10.2307/1992979
TAMS 82 (1956), No.1, 85-98
Description: Condition of vanishing of cohomology in all modules.
Availability: 1956-cohomology.pdf
Tensor product of semiprimary algebras
Duke M.J. 24 (1957), 555-559
Description: Tensor product of two unital semi-local algebras is semi-local.
Rosenberg, Alexander L.
Noncommutative Algebraic Geometry and Representations of Quantized Algebras
Kluwer, 1995
Zentralblatt: 0839.16002
Description: "Attempt to expose a new unifying approach to the study of numerous quantized algebras".
Availability: Kolkhoz
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Rosenberg, Jonathan
C*-algebras, positive scalar curvature, and the Novikov conjecture
Preprint, U. of Maryland, 1982
Availability: hardcopy
Algebraic K-Theory and Its Applications
Springer, 1994
Availability: google books
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Rosenberger, G.
Free subgroups of generalized triangle groups
Algebra and Logic 28 (1989), N2, 152-
Description: Tits alternative for such groups.
Availability: CWI
Rosenblatt, J.
Invariant measures and growth conditions
DOI: 10.2307/1996899
Trans. Amer. Math. Soc. 193 (1974), 33-53
Description: Any finitely generated solvable group contains a free semigroup on two generators unless it is virtually nilpotent. Various examples (including polycyclic) of groups containing free semigroup.
Availability: 1974-invariant.pdf
Rosenstein, J.G.
alpha_0-categoricity of groups
DOI: 10.1016/0021-8693(77)90305-2
J. Alg. 25 (1973), 435-467; Correction: Volume 48, Issue 2, October 1977, Pages 236-240
Description: A group is called alpha_0-categorical, if it can be characterized, up to isomorphism, within the class of all countable groups by its first-order properties; direct limist, direct sums, GL_2(B) over some ring B are involved
Rosenthal, Peter
Are almost commuting matrices near commuting matrices?
Amer. Math. Monthly 76 (1969), N8, 925-926
Description: Question: If A and B "almost" (in the sense of a metric) commute, does there exist nearby (in the same sense) matrices which commute?
Availability: matrices.pdf
Rosinger, E.E.
Short introduction to Nonstandard Analysis
math.GM/0407178
Ross, Leonard E.
Representations of Graded Lie Algebras
Transactions of the American Mathematical Society, Vol. 120, No. 1 (Oct., 1965), pp. 17-23
Description: Ado theorem for graded (super?) Lie algebras.
Rosellen, Markus
A Course in Vertex Algebra
math.QA/0607270, 204 pp.
Rosset, Myriam and Rosset, Shmuel
Elements of trace zero in central simple algebras
Rings, Extensions and Cohomology, Lect. Notes Pure Appl. Math. 159 (1994), 205-211
MR 95h:16022
Zentralblatt: 813.16011
Description: Every element of trace zero in a central simple algebra is represented as a sum of two commutator where two elements are prescribed (whenere they are for a so-called generic pair).
Availability: VU, UVA, CWI: absent; TUDelft: CB C194-1364; google print; trace-zero.tar (except page 206)
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Elements of trace zero which are not commutators
Comm. Alg. 28 (2000), N6, 3059-3072
MR 2001c:16055
Zentralblatt: 0954.16021
Description: Examples of 2x2 matrices over rings (some factorrings of k[x,y,z] and such) of trace 0 and which are not commutators.
Availability: hardcopy
Rosset, Shmuel and Wasserman, Alon
The Schreier technique for subalgebras of a free Lie algebra
CJM 49(1977), 600-
MR 98g:17003
Zentralblatt: 0973.17006
Description: Bases in free Lie algebra, Lazard's elimination theorem, subalgebras of free Lie algebras
Availability: CJM web site (file rosset0531.ps) (?)
Rost, Markus
On the dimension of a composition algebra
Documenta Math. 1(1996), 209-214
Abstract: The possible dimensions of a composition algebra are 1, 2, 4, or 8. We give a tensor categorical argument.
Rote, Günter and Vegter, Gert
Computational Topology: An Introduction
DOI: 10.1007/978-3-540-33259-6_7
Effective Computational Geometry for Curves and Surfaces (ed. Jean-Daniel Boissonnat and Monique Teillaud)
Rothmaler, P.
Einführung in die Modelltheorie
Spektrum, 1995; paperback, 331 pp.
Availability: hardcopy (book)
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Rotkiewicz, Mikolaj
On strong n-Lie-Poisson algebras
J. Pure Appl. Algebra 200 (2005), N1-2, 87-96
Description: The notions of strong n-Lie-Poisson and n-Lie-Poisson algebras coincide if and only if n is odd. This is the answer to a problem of Dzhumadil'daev.
Cohomology ring of n-Lie algebras
Extracta Math. 20 (2005), no. 3, 219--232
Rousseau, G.
On forms of Kac-Moody algebras
Algebraic Groups and Their Generalizations (ed. William J. Haboush and Brian J. Parshall), Part 2, AMS, 1984
Rousseeuw, Peter J. and Molenberghs, Geert
Transformation of non positive semidefinite correlation matrices
DOI: 10.1080/03610928308831068
Communications in Statistics - Theory and Methods, Volume 22, Issue 4 1993 , pages 965 - 984
Description: Coposede; rather primitive.
Availability: prgm_ton.pdf
Rowan, William H.
Abelian extensions of algebras in congruence-modular varieties
math.RA/0005134, 30 pages
Abstract: We define abelian extensions of algebras in congruence-modular varieties. The theory is sufficiently general that it includes, in a natural way, extensions of R-modules for a ring R. We also define a cohomology theory, which we call clone cohomology, such that the cohomology group in dimension one is the group of equivalence classes of extensions.
Rowen, Louis Halle
Structure of rings with involution applied to generalized polynomial identities
CJM 27 (1975), N3, 573-584
Availability: hardcopy; google books
General polynomial identities. II
DOI: 10.1016/0021-8693(76)90228-3
J. Algebra 38 (1976), N2, 380-392
Description: Theorem 6. If A, B are left ideals of a ring, and A,B are PI, then A+B is PI.
Availability: 1976-general.pdf
Polynomial identities of nonassociative rings. Part I: The general structure theory of nonassiative rings, with emphasis on polynomial identities and central polynomials
Ill. J. M. 22 (1978), N3, 341-378
Availability: hardcopy
Polynomial identities of nonassociative rings. Part II: Fine points of the structure theory
Ill. J. M. 22 (1978), N4, 521-540
Availability: hardcopy
Polynomial identities of nonassociative rings. Part III: Applications
Ill. J. M. 23 (1979), N1, 15-35
Availability: hardcopy
Nonassociative rings satisfying normal polynomial identities
J. Alg. 49 (1977), N1, 104-111
Availability: hardcopy
Polynomial Identities in Ring Theory
DOI: 10.1090/S0273-0979-1981-14949-1
Acedemic Press, 1980
Zentralblatt: 0461.16001
Review: Bull. Amer. Math. Soc. 5 (1981), 329-330
Availability: absent in Icelandic libraries
Ring Theory. II
DOI: 10.1090/S0273-0979-1989-15762-5
Academic Press, 1988
Review: Bull. Amer. Math. Soc. 20 (1989), 196-198
Description: Also PI.
Availability: absent in Icelandic libraries
K-Theory
Lecture Notes, Bar-Ilan U., 35pp.
Availability: hardcopy
Division algebras
Proc. Third Int. Algebra Conf., Chang Jung Christian Univ., Tainan, Taiwan (ed. Y. Fong, L.-S. Shiao, E. Zelmanov), Springer, 2003, 221-233
Description: A survey.
Availability: div.tar (few pages are missing)
google books
Review of "Polynomial Identity Rings" by Drensky and Formanek
DOI: 10.1090/S0273-0979-06-01082-2
BAMS 43 (2006), N2, 259-267
Description: An excellent historical account of the subject.
Availability: hardcopy (journal)
Graduate Algebra: Noncommutative View
AMS, 2008
Description: Including Tits alternative, PI algebras.
Roy, Amit
On a characterisation of Clifford algebras.
Math. Z. 85 1964 241--244.
29 #4778
Abstract: Sridharan [Trans. Amer. Math. Soc. 100 (1961), 530--550; MR 24 #A754] considered filtered algebras over a commutative ring $K$ whose associated graded algebras are isomorphic to the symmetric algebra of a free $K$-module $M$. He showed that such algebras are suitable generalisations of enveloping algebras of Lie algebra structures on $M$. In this note we ask an analogous question: namely, that of determining filtered algebras whose associated graded algebras are isomorphic to the exterior algebra on a free $K$-module $M$. If $Q$ is a quadratic form on $M$, it is easily verified (Proposition 1) that the Clifford algebra of $Q$ is an algebra of this type. We prove here that if 2 is invertible in $K$, any filtered algebra whose associated graded algebra is isomorphic to the exterior algebra on $M$ is in fact a Clifford algebra.
Roy, A. and Sridharan, R.
Higher derivations and central simple algebras
Nagoya Math. J. 32 (1968), 21-30
MR 0229681
Zentralblatt: 0159.05202
Description: Higher derivations in terms of certain filtered modules and related to certain second cohomology.
Royon, Yvan and Frénot, Stéphane
A survey of Unix init schemes
0706.2748
Roytenberg, Dmitry
On weak Lie 2-algebras
arXiv:0712.3461
Description: Generalization of Baez-Crans classification of 2-algebras through Leibniz 3rd degree cohomology of ordinary Lie algebras. Relationship between ordinary and Leibniz 3rd degree cohomology of Lie alegbras.
Rozanov, Y.A.
Probability Theory: A Concise Course
Dover, 1977 (slightly corrected republication of Prentice Hall, 1969); paperback, 148 pp.
Availability: hardcopy (book)
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Rozenfeld, B.I.
Cohomology of the algebra of formal universal differential operators
DOI: 10.1007/BF01075449
Funct. Anal. Appl. 9 (1975), 126-130
Description: In the spirit of Gelfand-Fuchs cohomology; reasonings about Hochschild-Serre spectral sequnce relating cohomology of a Lie algebra and its split extension.
Availability: hardcopy
Rozenfeld, B.A. and Karpova, L.M.
Flagovye gruppy i szhatie grupp Lie
Trudy Sem. Vekt. Tenz. Anal. 13 (1966), 168-202
Description: Contractions of simple compact Lie algebras.
Rozenfeld, B.A. and Zamakhovskii, M.P.
Prostye i kvaziprostye jordanovy algebry
Izv. VUZ 1971, N8, 111-121
Zentralblatt: absent
Description: Some special contractions of simple Jordan algebars over C and R.
Availability: hardcopy
Rubel, Lee A.
Conformal inequivalence of annuli and the first-order theory of subgroups of PSL(2, R)
Proc. AMS 88 (1983), No.4., 679-683.
Availability: 1983-conformal.pdf
Rudakov, A.N.
Groups of automorphisms of infinite-dimensional simple Lie algebras
Math. USSR Izv. 3 (1969), 707-722
Zentralblatt: 0222.17014
Description: Of Cartan types; also forms.
Availability: hardcopy
On representations of classical semisimple Lie algebras of characteristic p
Math. USSR Izv. 4 (1970), 741-749
Zentralblatt: 0242.17005
Deformations of simple Lie algebras
DOI: 10.1070/IM1971v005n05ABEH001204
Math. USSR Izv. 5 (1971), 1120-1126
MR 291235
Zentralblatt: 0257.17006
Description: p>3. Th. 1. If H^2(L,L), then Lie(Aut(L)) = Der(L). Corollary. If L is simple modular Lie algebra and H^2(L,L) = 0, then L is of classical type. Th. 2. If L is a modular Lie algebra of classical type, then H^2(L,L) = 0.
Availability: hardcopy
Irreducible representations of infinite-dimensional Lie algebras of Cartan type
Math. USSR Izv. 8 (1974), 836-866
Zentralblatt: 0322.17004
Local universal algebras and reduced representations of Lie algebras
Math. USSR Izv. 14 (1980), 169-174
Zentralblatt: 0428.17004
A condition for the complete reducibility of a representation of a Lie algebra of finite characteristic
Algebra, Collect., Moskva 1980, 77-82
Zentralblatt: 0471.17002
Reducible p-representations of simple three-dimensional Lie p-algebra
Mosc. Univ. Math. Bull. 37 (1982), No.6, 51-56
Zentralblatt: 0506.17004
Availability: hardcopy
Subalgebras and automorphisms of Lie algebras of Cartan type
Funct. Anal. Appl. 20 (1986), 72-73
Zentralblatt: 0594.17015
Description: Infinite-dimensional Lie algebras of Cartan type W_n, S_n, H_n, K_n over C: do not have subalgebras of codimension less than n; every subalgeba of codimension n coincides with L_0; have only continious isomorphisms; do not have nontrivial forms.
Availability: hardcopy
Rudakov, A.N. and Shafarevich, I.R.
Irreducilble representations of a simple three-dimensional Lie algebra over a field of finite characteristic
DOI: 10.1007/BF01093935
Math. Notes 2(1967), 760-767
Zentralblatt: 0184.06002
Availability: hardcopy; collected-works-3-2.djvu
Ruiter, J. de
On derivations of Lie algebras
Compositio Mathematica, 28 no. 3 (1974), p. 299-303
MR 364376
Zentralblatt: 0289.17011
Russell, B.
Introduction to Mathematical Philosophy
Dover, 1993; paperback, 208 pp.
Availability: hardcopy (book)
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Rutherford, D.E.
Substitutional Analysis
Edinburgh Univ. Press, 1948
Availability: rutherford_reprs.pdf
Ruzsa, Imre Z. and Szekely, Gabor J.
Algebraic probability theory
Wiley, 1988
Description: Probability theory in terms of the abstract theory of topological semigroups.
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Ryabukhin, Yu.M. and Florya, R.S.
Simple relatively free rings and minimal varieties of rings
Mat. Issled. 62 (1981), 112-129
MR 82g:17001
Description: An example of a nonassociative ring which does not lie in a variety generated by its proper quotient rings.
Ryan, John Gerard
Extensions of representations of Lie algebras.
Pacific J. Math. Volume 127, Number 1 (1987), 173-186
MR 876024
Zentralblatt: 0637.17002
Description: p=0. Let f:L->M be morhism of finite-dimensioanl Lie algebras. When a finite-dimensional L-module embeds into L-submodule of N-module?
Ryba, Alexander J.E.
Computer construction of split Cartan subalgebras
DOI: 10.1016/j.jalgebra.2006.04.038
Journal of Algebra Volume 309, Issue 2 , 15 March 2007, Pages 455-483
Rybnikov, L G
Centralizers of certain quadratic elements in Poisson-Lie algebras and the method of translation of invariants
Russ. Math. Surv. 60 (2005), N2, 367-369
Description: S(g)^g for a complex semisimple Lie algebra g. Poisson structure on S(g).
Availability: rm_60_367.pdf
Rychkov, S.V.
On extensions of modules
Russ. Math. Surv. 39 (1984), No.1, 181-182
Availability: hardcopy
Rylands, L. J. and Taylor, D. E.
Constructions for Octonion and Exceptional Jordan Algebras
DOI: 10.1023/A:1008399914122
Designs, Codes and Cryptography Volume 21, Numbers 1-3 / October, 2000 Pages 191-203
Ryll-Nardzewski, C.
On the categoricity in power <= aleph_0
Bull. Acad. Polon. Sci. Ser. Sci. Math. Astron. Phys. 7 (1959), 545-548
Description: A countable structure M is alpha_0-categorical iff Aut(M) has a finite number of orbits on an n-fold direct product of M for every n>0.
Ryzhkov, Ilya I.
On the normalizers of subalgebras in an infinite Lie algebra
Commun. Nonlinear Sci. Numer. Simul. 11 (2006), no. 2, 172--185
Description: An algorithm for calculating the normalizer of subalgebra in an infinite Lie symmetry algebra.
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