Group graded PI-algebras and their codimension growth
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(We) denote the codimension growth of W and of the identity component We, respectively. The following inequality had been conjectured by Bahturin and Zaicev: exp(W)≤ |G|2 exp(We). 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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