### Abstract

This paper concerns preprojective representations of a finite connected valued quiver without oriented cycles. For each such representation, 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 representation. The set of equivalence classes of the above sequences is a partially ordered set that contains a great deal of information about the preprojective component of the Auslander-Reiten quiver. The results apply to the study of reduced words in the Weyl group associated with an indecomposable symmetrizable generalized Cartan matrix.

Original language | English (US) |
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Pages (from-to) | 718-726 |

Number of pages | 9 |

Journal | Journal of Pure and Applied Algebra |

Volume | 212 |

Issue number | 4 |

DOIs | |

State | Published - Apr 2008 |

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

*Journal of Pure and Applied Algebra*,

*212*(4), 718-726. https://doi.org/10.1016/j.jpaa.2007.06.014