On the codimension growth of G-graded algebras
Abstract
Let W be an associative PI-affine 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. We prove: exp(W) ≤ |G|2 exp(We). This inequality had been conjectured by Bahturin and Zaicev.
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