The Coarse Structure of the Representation Algebra of a Finite Monoid. (30th January 2014)

• Record Type: Journal Article
• Authors: Schaps, Mary
• Other Names: Bergeron Nantel Academic Editor.
• Is Part Of: Journal of discrete mathematics. Volume 2014(2014)
• Publication Date: 2014-01-30
• Subjects: Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Periodicals; 511.1
• DOI: 10.1155/2014/529804
• Languages: English
• ISSNs: 2090-9837

Abstract

Abstract : LetM be a monoid, and letL be a commutative idempotent submonoid. We show that we can find a complete set of orthogonal idempotentsL ^ 0 of the monoid algebraA ofM such that there is a basis ofA 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 toL ^ 0 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.