Graded algebras with polynomial growth of their codimensions

Daniela La Mattina, Plamen Koshlukov

Risultato della ricerca: Articlepeer review

11 Citazioni (Scopus)

Abstract

Let A be an algebra over a field of characteristic 0 and assume A is graded by a finite group G. We study combinatorial and asymptotic properties of the G-graded polynomial identities of A provided A is of polynomial growth of the sequence of its graded codimensions. Roughly speaking this means that the ideal of graded identities is "very large". We relate the polynomial growth of the codimensions to the module structure of the multilinear elements in the relatively free G-graded algebra in the variety generated by A. We describe the irreducible modules that can appear in the decomposition, we show that their multiplicities are eventually constant depending on the shape obtained by the corresponding multipartition after removing its first row. We relate, moreover, the polynomial growth to the colengths. Finally we describe in detail the algebras whose graded codimensions are of linear growth.
Lingua originaleEnglish
pagine (da-a)115-137
Numero di pagine23
RivistaJournal of Algebra
Volume434
Stato di pubblicazionePublished - 2015

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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