Admissible sequences and the preprojective component of a quiver |
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Authors: | Mark Kleiner Helene R. Tyler |
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Affiliation: | a Department of Mathematics, Syracuse University, Room 215, Carnegie Hall, Syracuse, NY 13244-1150, USA b Department of Mathematics and Computer Science, Manhattan College, Riverdale, NY 10471, USA |
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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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Keywords: | 16G20 16G70 |
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