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arXiv · 1002.1385

Group graded PI-algebras and their codimension growth

Eli Aljadeff
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Abstract

Let W be an associative PI-algebra over a field F of characteristic zero. Suppose W is G-graded where G is a finite group. Let exp(W) and exp(W_e) denote the codimension growth of W and of the identity component W_e, respectively. The following inequality had been conjectured by Bahturin and Zaicev: exp(W)\leq |G|^2 exp(W_e). The inequality is known in case the algebra W is affine (i.e. finitely generated). Here we prove the conjecture in general.

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Eli Aljadeff. 2010-02-06. Group graded PI-algebras and their codimension growth. https://arxiv.org/abs/1002.1385

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