The Quiver of the Semigroup Algebra of a Left Regular Band
| dc.creator | Saliola, Franco V. | |
| dc.date | 2006-08-28 | |
| dc.date.accessioned | 2026-07-07T07:22:15Z | |
| dc.date.available | 2026-07-07T07:22:15Z | |
| dc.description | Recently it has been noticed that many interesting combinatorial objects belong to a class of semigroups called left regular bands, and that random walks on these semigroups encode several well-known random walks. For example, the set of faces of a hyperplane arrangement is endowed with a left regular band structure. This paper studies the module structure of the semigroup algebra of an arbitrary left regular band, extending results for the semigroup algebra of the faces of a hyperplane arrangement. In particular, a description of the quiver of the semigroup algebra is given and the Cartan invariants are computed. These are used to compute the quiver of the face semigroup algebra of a hyperplane arrangement and to show that the semigroup algebra of the free left regular band is isomorphic to the path algebra of its quiver. | |
| dc.description | 24 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math/0608698 | |
| dc.identifier | http://arxiv.org/abs/math/0608698 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115592 | |
| dc.subject | Combinatorics | |
| dc.subject | Rings and Algebras | |
| dc.subject | Representation Theory | |
| dc.subject | 05E99, 16S99 (Primary) 52C35 (Secondary) | |
| dc.title | The Quiver of the Semigroup Algebra of a Left Regular Band | |
| dc.type | text |