The polynomial part of the codimension growth of affine PI algebras

Eli Aljadeff, Geoffrey Janssens, Yakov Karasik*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Let F be a field of characteristic zero and W an associative affine F-algebra satisfying a polynomial identity (PI). The codimension sequence {cn(W)} associated to W is known to be of the form Θ(ntdn), where d is the well known PI-exponent of W. In this paper we establish an algebraic interpretation of the polynomial part (the constant t) by means of Kemer's theory. In particular, we show that in case W is a basic algebra (hence finite dimensional), t=q−d2+s, where q is the number of simple component in W/J(W) and s+1 is the nilpotency degree of J(W) (the Jacobson radical of W). Thus proving a conjecture of Giambruno.

Original languageEnglish
Pages (from-to)487-511
Number of pages25
JournalAdvances in Mathematics
Volume309
DOIs
StatePublished - 17 Mar 2017
Externally publishedYes

Keywords

  • Codimension sequence
  • Kemer polynomials
  • Polynomial identity

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