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On the codimension growth of G-graded algebras.

Tue, 08/18/2009 - 11:53 — SomNambul
Authors: Eli Aljadeff
Subjects: Rings and Algebras
link: http://arxiv.org/abs/0908.2385
Abstract

Let W be an associative PI affine algebra over a field F of characteristic
zero. Suppose W is G-graded where G a finite group. Let exp(W) and exp(W_e)
denote the codimension growth of W and W_e respectively. (Here W_e,(e in G)
denotes the identity component of W.) We prove: exp(W) is bounded (from above)
by ord(G)^2 exp(W_{e}). This was conjectured by in Y. A. Bahturin and M. V.
Zaicev, Identities of graded algebras and codimension growth, Trans. Amer.
Math. Soc. {356} (2004), no. 10, 3939--3950.

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