### 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 language | English (US) |
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Pages (from-to) | 376-402 |

Number of pages | 27 |

Journal | Advances in Mathematics |

Volume | 192 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1 2005 |

### Keywords

- Admissible sequence
- Preprojective module
- Quiver
- Slice

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

*Advances in Mathematics*,

*192*(2), 376-402. https://doi.org/10.1016/j.aim.2004.04.006