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Admissible sequences and the preprojective component of a quiver

Authors
  • Kleiner, Mark
  • Tyler, Helene R.
Type
Published Article
Journal
Advances in Mathematics
Publication Date
Jan 01, 2004
Accepted Date
Apr 23, 2004
Volume
192
Issue
2
Pages
376–402
Identifiers
DOI: 10.1016/j.aim.2004.04.006
Source
Elsevier
Keywords
License
Unknown

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.

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