Serdica Mathematical Journal

Volume 38, Numbers 1-3, 2012





C O N T E N T S

Preface (pp. i-ii)
Scientific Program (pp. iii-iv)
List of Participants (pp. v-vii)
Professor Yuri Bahturin (on his 65th birthday) (pp. vii-viii)
Students of Yuri Bahturin (pp. ix-x)
List of Books, Papers, Translated Books and Edited Volumes of Yuri Bahturin (pp. xi-xxii)

Bahturin, Yu. Group gradings on free algebras of nilpotent varieties of algebras (pp. 1-6)
Elduque, A., M. Kochetov. Weyl groups of fine gradings on simple Lie algebras of types A, B, C and D (pp. 7-36)
Parmenter, M. M. Pancyclic Cayley graphs (pp. 37-42)
Centrone, L. On some recent results about the graded Gelfand-Kirillov dimension of graded PI-algebras (pp. 43-68)
Berele, A. Some questions about products of verbally prime T-ideals (pp. 69-78)
Rashkova, Ts. On the nilpotency in matrix algebras with Grassmann entries (pp. 79-90)
Bremner, M. R. Algebras, dialgebras, and polynomial identities (pp. 91-136)
Benanti, F., S. Boumova, V. Drensky, G. K. Genov, P. Koev. Computing with rational symmetric functions and applications to invariant theory and PI-algebras (pp. 137-188)
Koshlukov, P., J. César dos Reis. Gradings and graded identities for the matrix algebra of order two in characteristic 2 (pp. 189-198)
Bresar, M. A unified approach to the structure theory of PI-rings and GPI-rings (pp. 199-210)
Volichenko, I. B.
, A. E. Zalesskii. Characterization of certain T-ideals from the view point of representation theory of the symmetric groups (pp. 211-236)
La Mattina, D. Varieties of superalgebras of polynomial growth (pp. 237-258)
Gordienko, A. S. Asymptotic behaviour of functional identities (pp. 259-272)
Findik, S. Outer automorphisms of Lie algebras related with generic 2×2 matrices (pp. 273-296)
Brandão, A. P. Jr., D. José Gonçalves. Central A-polynomials for the Grassmann algebra (pp. 297-312)
Belov-Kanel, A., L. Rowen, U. Vishne. Full exposition of Specht's problem (pp. 313-370)
Giambruno, A., S. Mishchenko, M. Zaicev. Some numerical invariants of multilinear identities (pp. 371-394)
Budrevich, M. V., A. E. Guterman. On the Gibson bounds over finite fields (pp. 395-416)
da Silva, V. R. T. On ordinary and Z2-graded polynomial identities of the Grassmann algebra (pp. 417-432)
Tvalavadze, M. Universal enveloping algebras of nonassociative structures (pp. 433-462)
Lomond, J. Growth functions of Fr-sets (pp. 463-472)
Finogenova, O. Characterizing non-matrix properties of varieties of algebras in the language of forbidden objects (pp. 473-496)
Koshlukov, P., A. Krasilnikov. A basis for the graded identities of the pair (M2(K), gl2(K)) (pp. 497-506)


A B S T R A C T S


GROUP GRADINGS ON FREE ALGEBRAS OF NILPOTENT VARIETIES OF ALGEBRAS
Yuri Bahturin bahturin@mun.ca

2010 Mathematics Subject Classification: Primary 16W50, 17B70; Secondary 16R10.
Key words: graded algebra, nilpotent Lie algebra, grading.


WEYL GROUPS OF FINE GRADINGS ON SIMPLE LIE ALGEBRAS OF TYPES A, B, C AND D
Alberto Elduque elduque@unizar.es,
Mikhail Kochetov mikhail@mun.ca

2010 Mathematics Subject Classification: Primary 17B70, secondary 17B40, 16W50.
Key words: Graded algebra, fine grading, Weyl group, simple Lie algebra.


PANCYCLIC CAYLEY GRAPHS
M. M. Parmenter mparmen@mun.ca

2010 Mathematics Subject Classification: Primary 05C25. Secondary 20K01, 05C45.
Key words: Cayley graph, Pancyclic, Abelian group.


ON SOME RECENT RESULTS ABOUT THE GRADED GELFAND-KIRILLOV DIMENSION OF GRADED PI-ALGEBRAS
Lucio Centrone centrone@ime.unicamp.br

2010 Mathematics Subject Classification: 16R10, 16W55, 15A75.
Key words: graded PI-algebras, Gelfand-Kirillov dimension.


SOME QUESTIONS ABOUT PRODUCTS OF VERBALLY PRIME T-IDEALS
Allan Berele aberele@condor.depaul.edu

2010 Mathematics Subject Classification: 16R10.
Key words: incidence algebras, polynomial identities, verbally prime T-ideals.


ON THE NILPOTENCY IN MATRIX ALGEBRAS WITH GRASSMANN ENTRIES
Tsetska Rashkova tsrashkova@uni-ruse.bg

2010 Mathematics Subject Classification: 16R10, 15A75, 16S50.
Key words: Polynomial identity, upper triangular matrices, nilpotent commutators, index of nilpotency.


ALGEBRAS, DIALGEBRAS, AND POLYNOMIAL IDENTITIES
Murray R. Bremner bremner@math.usask.ca

2010 Mathematics Subject Classification: Primary 17A30. Secondary 16R10, 17-08, 17A32, 17A40, 17A50, 17B60, 17C05, 17D05, 17D10.
Key words: Algebras, triple systems, dialgebras, triple disystems, polynomial identities, multilinear operations, computer algebra.


COMPUTING WITH RATIONAL SYMMETRIC FUNCTIONS AND APPLICATIONS TO INVARIANT THEORY AND PI-ALGEBRAS
Francesca Benanti fbenanti@math.unipa.it,
Silvia Boumova silvi@math.bas.bg,
Vesselin Drensky drensky@math.bas.bg,
Georgi K. Genov guenovg@mail.bg,
Plamen Koev plamen.koev@sjsu.edu

2010 Mathematics Subject Classification: 05A15, 05E05, 05E10, 13A50, 15A72, 16R10, 16R30, 20G05.
Key words: Rational symmetric functions, MacMahon partition analysis, Hilbert series, classical invariant theory, noncommutative invariant theory, algebras with polynomial identity, cocharacter sequence.


GRADINGS AND GRADED IDENTITIES FOR THE MATRIX ALGEBRA OF ORDER TWO IN CHARACTERISTIC 2
Plamen Koshlukov plamen@ime.unicamp.br,
Júlio César dos Reis jcreis@ime.unicamp.br

2010 Mathematics Subject Classification: 16R10, 16R99, 16W50.
Key words: gradings on matrix algebras, graded identities, polynomial identities in characteristic two.


A UNIFIED APPROACH TO THE STRUCTURE THEORY OF PI-RINGS AND GPI-RINGS
Matej Bresar matej.bresar@fmf.uni-lj.si

2010 Mathematics Subject Classification: 16R20, 16R50, 16R60, 16N60.
Key words: polynomial identity, generalized polynomial identity, functional identity, prime ring, extended centroid, symmetric Martindale ring of quotients.


CHARACTERIZATION OF CERTAIN T-IDEALS FROM THE VIEW POINT OF REPRESENTATION THEORY OF THE SYMMETRIC GROUPS
I. B. Volichenko
A. E. Zalesskii alexandre.zalesski@gmail.com

2010 Mathematics Subject Classification: 08B20, 16R10, 16R40, 20C30.
Key words: T-ideals, Free associative algebras.


VARIETIES OF SUPERALGEBRAS OF POLYNOMIAL GROWTH
Daniela La Mattina daniela.lamattina@unipa.it

2010 Mathematics Subject Classification: 16R10, 16W55, 16P90.
Key words: polynomial identity, growth, superalgebra.


ASYMPTOTIC BEHAVIOUR OF FUNCTIONAL IDENTITIES
A. S. Gordienko asgordienko@mun.ca

2010 Mathematics Subject Classification: Primary 16R60, Secondary 16R10, 15A03, 15A69.
Key words: Functional identity, generalized functional identity, codimension, growth, algebra, Amitsur's conjecture, Regev's conjecture.


OUTER AUTOMORPHISMS OF LIE ALGEBRAS RELATED WITH GENERIC 2×2 MATRICES
Sehmus Findik sfindik@cu.edu.tr

2010 Mathematics Subject Classification: 17B01, 17B30, 17B40, 16R30.
Key words: free Lie algebras, generic matrices, inner automorphisms, outer automorphisms.


CENTRAL A-POLYNOMIALS FOR THE GRASSMANN ALGEBRA
Antônio Pereira Brandão Jr. brandao@dme.ufcg.edu.br,
Dimas José Gonçalves dimasjog@gmail.com

2010 Mathematics Subject Classification: 16R10, 16R40, 16R50.
Key words: A-identity, central A-polynomial, Grassmann algebra.


FULL EXPOSITION OF SPECHT'S PROBLEM
Alexei Belov-Kanel belova@macs.biu.ac.il,
Louis Rowen rowen@macs.biu.ac.il,
Uzi Vishne vishne@macs.biu.ac.il

2010 Mathematics Subject Classification: Primary: 16R10; Secondary: 16R30, 17A01, 17B01, 17C05.
Key words: Specht's question, polynomial identities, T-ideal, affine algebra, representable algebra, torsion, Noetherian.


SOME NUMERICAL INVARIANTS OF MULTILINEAR IDENTITIES
Antonio Giambruno antonio.giambruno@unipa.it,
Sergey Mishchenko mishchenkosp@ulsu.ru,
Mikhail Zaicev zaicevmv@mail.ru

2010 Mathematics Subject Classification: Primary 16R10, 16A30, 16A50, 17B01, 17C05, 17D05, 16P90, 17A, 17D.
Key words: Polynomial identity, codimensions, colengths.


ON THE GIBSON BOUNDS OVER FINITE FIELDS
Mikhail V. Budrevich mbudrevich@yandex.ru,
Alexander E. Guterman guterman@list.ru

2010 Mathematics Subject Classification: 15A15, 15A04.
Key words: permanent, determinant, finite fields, Pólya problem.


ON ORDINARY AND $\Z_2$-GRADED POLYNOMIAL IDENTITIES OF THE GRASSMANN ALGEBRA
Viviane Ribeiro Tomaz da Silva viviane@mat.ufmg.br

2010 Mathematics Subject Classification: Primary: 16R10, Secondary: 16W55.
Key words: Ordinary polynomial identities, graded polynomial identities, cocharacters, codimensions, Grassmann algebra.


UNIVERSAL ENVELOPING ALGEBRAS OF NONASSOCIATIVE STRUCTURES
Marina Tvalavadze mtvalava@fields.utoronto.ca

2010 Mathematics Subject Classification: Primary 17D15. Secondary 17D05, 17B35, 17A99.
Key words: Malcev algebras, Leibniz algebras, triple systems, universal enveloping algebras, PBW-bases.


GROWTH FUNCTIONS OF Fr-SETS
Jonny Lomond jjl831@mun.ca

2010 Mathematics Subject Classification: 05C30, 20E08, 20F65.
Key words: Group action, growth function.


CHARACTERIZING NON-MATRIX PROPERTIES OF VARIETIES OF ALGEBRAS IN THE LANGUAGE OF FORBIDDEN OBJECTS
Olga Finogenova olgafinogenova@gmail.com

2010 Mathematics Subject Classification: 16R10, 16R40.
Key words: algebras with polynomial identity, non-matrix varieties, Engel property, Lie nilpotency, semigroup identities, forbidden algebras, varieties of associative algebras.


A BASIS FOR THE GRADED IDENTITIES OF THE PAIR (M2(K), gl2(K))
Plamen Koshlukov plamen@ime.unicamp.br,
Alexei Krasilnikov alexei@unb.br

2010 Mathematics Subject Classification: 16R10, 17B01.
Key words: Graded identities, weak identities, basis of graded identities.


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