Minimal projective resolutions

E. L. Green, Solberg, D. Zacharia

Research output: Contribution to journalArticlepeer-review

34 Scopus citations

Abstract

In this paper, we present an algorithmic method for computing a protective resolution of a module over an algebra over a field. If the algebra is finite dimensional, and the module is finitely generated, we have a computational way of obtaining a minimal projective resolution, maps included. This resolution turns out to be a graded resolution if our algebra and module are graded. We apply this resolution to the study of the Ext-algebra of the algebra; namely, we present a new method for computing Yoneda products using the constructions of the resolutions. We also use our resolution to prove a case of the "no loop" conjecture.

Original languageEnglish (US)
Pages (from-to)2915-2939
Number of pages25
JournalTransactions of the American Mathematical Society
Volume353
Issue number7
DOIs
StatePublished - 2001

Keywords

  • Finite dimensional and graded algebras
  • Projective resolutions

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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