Paper Info
Title
Möbius functions and semigroup representation theory
Abstract
This paper explores several applications of Möbius functions to the representation theory of finite semigroups. We extend Solomon's approach to the semigroup algebra of a finite semilattice via Möbius functions to arbitrary finite inverse semigroups. This allows us to explicitly calculate the orthogonal central idempotents decomposing an inverse semigroup algebra into a direct product of matrix algebras over group rings. We also extend work of Bidigare, Hanlon, Rockmore and Brown on calculating eigenvalues of random walks associated to certain classes of finite semigroups; again Möbius functions play an important role.
Year
DOI
Venue
2006
10.1016/j.jcta.2005.08.004
J. Comb. Theory, Ser. A
Keywords
Field
DocType
semigroup algebra,möbius functions,certain class,representation theory,finite semilattice,arbitrary finite inverse semigroups,inverse semigroups,bius function,matrix algebra,direct product,group ring,inverse semigroup algebra,random walks on semigroups,finite semigroups,semigroup algebras,semigroup representation theory,random walk
Discrete mathematics,Bicyclic semigroup,Combinatorics,Krohn–Rhodes theory,Cancellative semigroup,Algebra,Inverse semigroup,Inverse element,Special classes of semigroups,Semigroup,Matrix unit,Mathematics
Journal
Volume
Issue
ISSN
113
5
Journal of Combinatorial Theory, Series A
Citations 
PageRank 
References 
11
1.42
1
Authors
1
Name
Order
Citations
PageRank
Benjamin Steinberg110217.57