Comparison morphisms and the Hochschild cohomology ring of truncated quiver algebras

Guillermo Ames, Leandro Cagliero*, Paulo Tirao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

A main contribution of this paper is the explicit construction of comparison morphisms between the standard bar resolution and Bardzell's minimal resolution for truncated quiver algebras over arbitrary fields (TQA's). As a direct application we describe explicitly the Yoneda product and derive several results on the structure of the cohomology ring of TQA's over a field of characteristic zero. For instance, we show that the product of odd degree cohomology classes is always zero. We prove that TQA's associated with quivers with no cycles or with neither sinks nor sources have trivial cohomology rings. On the other side we exhibit a fundamental example of a TQA with nontrivial cohomology ring. Finally, for truncated polynomial algebras in one variable, we construct explicit cohomology classes in the bar resolution and give a full description of their cohomology ring.

Original languageEnglish
Pages (from-to)1466-1497
Number of pages32
JournalJournal of Algebra
Volume322
Issue number5
DOIs
StatePublished - 1 Sep 2009
Externally publishedYes

Keywords

  • Comparison morphisms
  • Cup product
  • Hochschild cohomology ring
  • Truncated quiver algebras

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