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Group graded PI-algebras and their codimension growth

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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(W e ) denote the codimension growth of W and of the identity component W e , respectively. The following inequality had been conjectured by Bahturin and Zaicev: exp(W) ≤ |G|2 exp(W e ). The inequality is known in case the algebra W is affine (i.e., finitely generated). Here we prove the conjecture in general.

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Authors and Affiliations

  1. Department of Mathematics, Technion-Israel Institute of Technology, Haifa, 32000, Israel

    Eli Aljadeff

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  1. Eli Aljadeff
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Correspondence to Eli Aljadeff.

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The author was partially supported by the Israel Science Foundation (grant no. 1283/08) and by the E. Schaver Research Fund.

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Aljadeff, E. Group graded PI-algebras and their codimension growth. Isr. J. Math. 189, 189–205 (2012). https://doi.org/10.1007/s11856-011-0156-8

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  • DOI: https://doi.org/10.1007/s11856-011-0156-8

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