On the codimension growth of 𝐺-graded algebras

Aljadeff, Eli

doi:10.1090/S0002-9939-10-10282-2

On the codimension growth of $G$-graded algebras
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Proc. Amer. Math. Soc. 138 (2010), 2311-2320 Request permission

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 $\exp (W_{e})$ denote the codimension growth of $W$ and of the identity component $W_{e}$, respectively. We prove $\exp (W)\leq |G|^2 \exp (W_{e}).$ This inequality had been conjectured by Bahturin and Zaicev.

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