Table of Contents
Journal of Discrete Mathematics
Volume 2014 (2014), Article ID 529804, 7 pages
http://dx.doi.org/10.1155/2014/529804
Research Article

The Coarse Structure of the Representation Algebra of a Finite Monoid

Department of Mathematics, Bar-Ilan University, 52900 Ramat Gan, Israel

Received 30 June 2013; Accepted 12 November 2013; Published 30 January 2014

Academic Editor: Nantel Bergeron

Copyright © 2014 Mary Schaps. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be a monoid, and let be a commutative idempotent submonoid. We show that we can find a complete set of orthogonal idempotents of the monoid algebra of such that there is a basis of adapted to this set of idempotents which is in one-to-one correspondence with elements of the monoid. The basis graph describing the Peirce decomposition with respect to gives a coarse structure of the algebra, of which any complete set of primitive idempotents gives a refinement, and we give some criterion for this coarse structure to actually be a fine structure, which means that the nonzero elements of the monoid are in one-to-one correspondence with the vertices and arrows of the basis graph with respect to a set of primitive idempotents, with this basis graph being a canonical object.