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Group-graded algebras with polynomial identity

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Abstract

LetG be a finite group and letR=Σ g∈G R g be any associative algebra over a field such that the subspacesR g satisfyR g R h ⊆R gh . We prove that ifR 1 satisfies a PI of degreed, thenR satisfies a PI of degree bounded by an explicit function ofd and the order ofG. This result implies the following: ifH is a finite-dimensional semisimple commutative Hopfalgebra andR is anyH-module algebra withR H satisfying a PI of degreed, thenR satisfies a PI of degree bounded by an explicit function ofd and the dimension ofH.

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Authors and Affiliations

  1. Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, 119899, Moscow, Russia

    Yuri Bahturin

  2. Dipartimento di Matematica ed Applicazioni, Università di Palermo, Via Archirafi, 34, 90123, Palermo, Italy

    Antonio Giambruno

  3. Department of Mathematics, The University of Alabama, 35487-0350, Tuscaloosa, AL, USA

    David M. Riley

Authors
  1. Yuri Bahturin
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  2. Antonio Giambruno
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  3. David M. Riley
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Correspondence to Yuri Bahturin.

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Bahturin, Y., Giambruno, A. & Riley, D.M. Group-graded algebras with polynomial identity. Isr. J. Math. 104, 145–155 (1998). https://doi.org/10.1007/BF02897062

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  • DOI: https://doi.org/10.1007/BF02897062

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