Admissible sequences and the preprojective component of a quiver

Mark Kleiner, Helene R. Tyler

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

This paper concerns indecomposable preprojective modules over the path algebra of a finite connected quiver without oriented cycles. For each such module, an explicit formula in terms of the geometry of the quiver gives a unique, up to a certain equivalence, shortest (+)-admissible sequence such that the corresponding composition of reflection functors annihilates the module. An efficient way to compute the module is to recover it from its shortest (+)-admissible sequence. The set of equivalence classes of the above sequences has a natural structure of a partially ordered set. For a large class of quivers, the Hasse diagram of the partially ordered set is isomorphic to the preprojective component of the Auslander-Reiten quiver. The techniques of (+)-admissible sequences yield a new result about slices in the preprojective component.

Original languageEnglish (US)
Pages (from-to)376-402
Number of pages27
JournalAdvances in Mathematics
Volume192
Issue number2
DOIs
StatePublished - Apr 1 2005

Keywords

  • Admissible sequence
  • Preprojective module
  • Quiver
  • Slice

ASJC Scopus subject areas

  • Mathematics(all)

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