Identities of graded algebras and codimension growth

Authors:
Yu. A. Bahturin and M. V. Zaicev

Translated by:

Journal:
Trans. Amer. Math. Soc. **356** (2004), 3939-3950

MSC (2000):
Primary 16R10, 16W50

DOI:
https://doi.org/10.1090/S0002-9947-04-03426-9

Published electronically:
January 16, 2004

MathSciNet review:
2058512

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a -graded associative algebra over a field of characteristic zero. In this paper we develop a conjecture that relates the exponent of the growth of polynomial identities of the identity component to that of the whole of , in the case where the support of the grading is finite. We prove the conjecture in several natural cases, one of them being the case where is finite dimensional and has polynomial growth.

**1.**Bergen, J. and Cohen, M.*Actions of commutative Hopf algebras*, Bull. London Math. Soc.,**18**(1986), 159-164. MR**87e:16052****2.**Bahturin, Y., Giambruno, A. and Riley, D.*Group-graded algebras with polynomial identity*, Israel J. Math.,**104**(1998), 145-155. MR**99c:16041****3.**Bahturin, Y., Zaicev M.*Identities of graded algebras*, J. Algebra,**205**(2001), 1-12. MR**99f:17034****4.**Regev, A.*Existence of identities in*, Israel J. Math.,**11**(1972), 131-152. MR**47:3442****5.**Giambruno, A. and Zaicev, M.*On codimension growth of finitely generated associative algebras*, Advances in Mathematics,**140**(1998), 145-155. MR**99k:16049****6.**Giambruno, A. and Zaicev, M.V.*Exponential codimension growth of P.I. algebras: an exact estimate*, Advances in Mathematics,**142**(1999), 221-243. MR**2000a:16048****7.**Giambruno, A. and Zaicev, M.*Minimal varieties of algebras of exponential growth*, Electron. Res. Announc. Amer. Math. Soc.**6**(2000), 40-44. MR**2001e:16037****8.**Taft, E.J.*Invariant Wedderburn factors*, Illinois J. Math.**1**(1957), 565-573. MR**20:4586****9.**Bahturin, Y., Sehgal, S.K. and Zaicev, M.*Group gradings on associative algebras*, J. Alg.,**241**(2001), 677-698. MR**2002h:16067****10.**Regev, A.*Codimensions and trace codimensions of matrices are asymptotically equal*, Israel J. Math.,**47**(1984), 246-250. MR**85j:16024****11.**Mal'cev, A.I.*On representability of infinite algebras*, Matem. Sb.,**13**(1943), 263-286. (Russian) MR**6:116c**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC (2000):
16R10,
16W50

Retrieve articles in all journals with MSC (2000): 16R10, 16W50

Additional Information

**Yu. A. Bahturin**

Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, Newfoundland, Canada A1A 5K9 – and – Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119899, Russia

Email:
yuri@math.mun.ca

**M. V. Zaicev**

Affiliation:
Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119899, Russia

Email:
zaicev@mech.math.msu.su

DOI:
https://doi.org/10.1090/S0002-9947-04-03426-9

Received by editor(s):
March 6, 2002

Received by editor(s) in revised form:
May 29, 2003

Published electronically:
January 16, 2004

Additional Notes:
The first author was partially supported by MUN Dean of Science Research Grant #38647

The second author was partially supported by RFBR, grants 99-01-00233 and 00-15-96128

Article copyright:
© Copyright 2004
American Mathematical Society