On the codimension growth of G-graded algebras

Eli Aljadeff

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

On the codimension growth of G-graded algebras

Eli Aljadeff^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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 We, respectively. We prove exp(W) ≤ |G|² exp(W _e). This inequality had been conjectured by Bahturin and Zaicev.

Original language	English
Pages (from-to)	2311-2320
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	138
Issue number	7
DOIs	https://doi.org/10.1090/S0002-9939-10-10282-2
State	Published - Jul 2010
Externally published	Yes

Keywords

Graded algebra
Polynomial identity

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10.1090/S0002-9939-10-10282-2

Cite this

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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(W e). This inequality had been conjectured by Bahturin and Zaicev.",

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AB - 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(W e). This inequality had been conjectured by Bahturin and Zaicev.

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KW - Polynomial identity

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ER -

On the codimension growth of G-graded algebras

Abstract

Keywords

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