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THE QUIVER OF THE SEMIGROUP ALGEBRA OF A LEFT REGULAR BAND.
- Source :
-
International Journal of Algebra & Computation . Dec2007, Vol. 17 Issue 8, p1593-1610. 18p. 2 Diagrams. - Publication Year :
- 2007
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ALGEBRA
*MATHEMATICS
*GROUP theory
*COMBINATORIAL group theory
*RANDOM walks
Subjects
Details
- Language :
- English
- ISSN :
- 02181967
- Volume :
- 17
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- International Journal of Algebra & Computation
- Publication Type :
- Academic Journal
- Accession number :
- 27943278
- Full Text :
- https://doi.org/10.1142/S0218196707004219