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arXiv · 1204.3159

Multialternating graded polynomials and growth of polynomial identities

Eli Aljadeff·Antonio Giambruno
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Abstract

Let G be a finite group and A a finite dimensional G-graded algebra over a field of characteristic zero. When A is simple as a G-graded algebra, by mean of Regev central polynomials we construct multialternating graded polynomials of arbitrarily large degree non vanishing on A. As a consequence we compute the exponential rate of growth of the sequence of graded codimensions of an arbitrary G-graded algebra satisfying an ordinary polynomial identity. In particular we show it is an integer. The result was proviously known in case G is abelian.

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Eli Aljadeff, Antonio Giambruno. 2012-04-14. Multialternating graded polynomials and growth of polynomial identities. https://arxiv.org/abs/1204.3159

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