Auslander-Reiten components containing modules with bounded Betti numbers

Edward L. Green, Dan Zacharia

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

Let R be a connected selfinjective Artin algebra, and M an indecomposable nonprojective R-module with bounded Betti numbers lying in a regular component of the Auslander-Reiten quiver of R. We prove that the Auslander-Reiten sequence ending at M has at most two indecomposable sum-mands in the middle term. Furthermore we show that the component of the Auslander-Reiten quiver containing M is either a stable tube or of type ℤA. We use these results to study modules with eventually constant Betti numbers, and modules with eventually periodic Betti numbers.

Original languageEnglish (US)
Pages (from-to)4195-4214
Number of pages20
JournalTransactions of the American Mathematical Society
Volume361
Issue number8
DOIs
StatePublished - Aug 1 2009

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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