Möbius functions and semigroup representation theory

Möbius Functions and Semigroup Representation Theory Ii: Character Formulas and Multiplicities

We generalize the character formulas for multiplicities of irreducible constituents from group theory to semigroup theory using Rota’s theory of Möbius inversion. The technique works for a large class of semigroups including: inverse semigroups, semigroups with commuting idempotents, idempotent semigroups and semigroups with basic algebras. Using these tools we are able to give a complete descr...

Möbius function of semigroup posets through Hilbert series

In this paper, we investigate the Möbius function μS associated to a (locally finite) poset arising from a semigroup S of Zm. We introduce and develop a new approach to study μS by using the Hilbert series of S. The latter enables us to provide formulas for μS when S belongs to certain families of semigroups. Finally, a characterization for a locally finite poset to be isomorphic to a semigroup...

THE LEFT REGULAR REPRESENTATION OF A COMMUTATIVE SEPARATIVE SEMIGROUP

In this paper, a commutative semigroup will be written as a disjoint union of its cancellative subsemigroups. Based on this fact we will define the left regular representation of a commutative separative semigroup and show that this representation is faithful. Finally concrete examples of commutative separative semigroups, their decompositions and their left regular representations are given.

A characterization of triple semigroup of ternary functions and Demorgan triple semigroup of ternary functions

SEMIGROUP ACTIONS , WEAK ALMOST PERIODICITY, AND INVARIANT MEANS

Let S be a topological semigroup acting on a topological space X. We develop the theory of (weakly) almost periodic functions on X, with respect to S, and form the (weakly) almost periodic compactifications of X and S, with respect to each other. We then consider the notion of an action of Son a Banach space, and on its dual, and after defining S-invariant means for such a space, we give a...