Rank varieties for a class of finite-dimensional local algebras

David John Benson, Karin Erdmann, Miles Holloway

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

We develop a rank variety for finite-dimensional modules over a certain class of finite-dimensional local k-algebras, A(q,m)(n). Included in this class are the truncated polynomial algebras k[X1,..., X-m]/(X-i(n)), with k an algebraically closed field and char(k) arbitrary. We prove that these varieties characterise projectivity of modules (Dade's lemma) and examine the implications for the tree class of the stable Auslander-Reiten quiver. We also extend our rank varieties to infinitely generated modules and verify Dade's lemma in this context.

Original languageEnglish
Pages (from-to)497-510
Number of pages14
JournalJournal of Pure and Applied Algebra
Volume211
Issue number2
Early online date25 Mar 2007
DOIs
Publication statusPublished - Nov 2007

Keywords

  • generalized clifford algebra
  • infinitely generated modules
  • support varieties
  • group schemes
  • lie-algebras
  • cohomology
  • complexity

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