Multialternating graded polynomials and growth of polynomial identities

Authors:
Eli Aljadeff and Antonio Giambruno

Journal:
Proc. Amer. Math. Soc. **141** (2013), 3055-3065

MSC (2010):
Primary 16R50, 16P90, 16R10, 16W50

Published electronically:
June 5, 2013

MathSciNet review:
3068959

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a finite group and a finite dimensional -graded algebra over a field of characteristic zero. When is simple as a -graded algebra, by means of Regev central polynomials we construct multialternating graded polynomials of arbitrarily large degree non-vanishing on . As a consequence we compute the exponential rate of growth of the sequence of graded codimensions of an arbitrary -graded algebra satisfying an ordinary polynomial identity. If , is the sequence of graded codimensions of , we prove that , the -exponent of , exists and is an integer. This result was proved by the authors and D. La Mattina in 2011 and by the second author and D. La Mattina in 2010 in the case is abelian.

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Additional Information

**Eli Aljadeff**

Affiliation:
Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel

Email:
aljadeff@tx.technion.ac.il

**Antonio Giambruno**

Affiliation:
Dipartimento di Matematica e Informatica, Università di Palermo, Via Archirafi 34, 90123 Palermo, Italy

Email:
antonio.giambruno@unipa.it

DOI:
https://doi.org/10.1090/S0002-9939-2013-11589-3

Keywords:
Graded algebra,
polynomial identity,
growth,
codimensions

Received by editor(s):
July 22, 2011

Received by editor(s) in revised form:
December 5, 2011

Published electronically:
June 5, 2013

Additional Notes:
The first author was supported by the Israel Science Foundation (grant No. 1283/08) and by the E. Schaver Research Fund

The second author was partially supported by MIUR of Italy

Communicated by:
Harm Derksen

Article copyright:
© Copyright 2013
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.