Group graded PI-algebras and their codimension growth

Eli Aljadeff*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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) ≤ {pipe}G{pipe}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.

Original languageEnglish
Pages (from-to)189-205
Number of pages17
JournalIsrael Journal of Mathematics
Volume189
Issue number1
DOIs
StatePublished - Jun 2012
Externally publishedYes

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