Graded polynomial identities and exponential growth

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Abstract

Let $A$ be a finite dimensional algebra over a fieldof characteristic zero graded by a finite abelian group $G$. Here westudy a growth function related to the graded polynomial identitiessatisfied by $A$ by computing the exponential rate of growth of thesequence of graded codimensions of $A$. We prove that the$G$-exponent of $A$ exists and is an integer related in an explicitway to the dimension of a suitable semisimple subalgebra of $A$.
Lingua originaleEnglish
pagine (da-a)83-100
Numero di pagine18
RivistaJOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK
Volume650
Stato di pubblicazionePublished - 2011

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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