Rigid quivers and rigid algebras

Leandro Cagliero, Paulo Tirao*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We define a quiver to be rigid if all the associated truncated quiver algebras are rigid. The rigidity of quivers is then determined by the combinatorics of the set of pairs of parallel paths of the underlying quiver as follows from Cibils' criteria for the rigidity of truncated quiver algebras. In this paper we characterize rigid quivers Δ and relate this characterization with the condensed quiver and the quiver of beads of Δ, two much simpler quivers associated to Δ. The first one is a well-known object and the second one is introduced by us to this end.

Original languageEnglish
Pages (from-to)2827-2846
Number of pages20
JournalJournal of Algebra
Volume320
Issue number7
DOIs
StatePublished - 1 Oct 2008
Externally publishedYes

Keywords

  • Combinatorics of quivers
  • Deformations of algebras
  • Hochschild cohomology of truncated quiver algebras

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