Representation Theory of Compact Inverse Semigroups

Representation Theory of Compact Inverse Semigroups

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Title: Representation Theory of Compact Inverse Semigroups
Author: Hajji, Wadii
Abstract: W. D. Munn proved that a finite dimensional representation of an inverse semigroup is equivalent to a ⋆-representation if and only if it is bounded. The first goal of this thesis will be to give new analytic proof that every finite dimensional representation of a compact inverse semigroup is equivalent to a ⋆-representation. The second goal is to parameterize all finite dimensional irreducible representations of a compact inverse semigroup in terms of maximal subgroups and order theoretic properties of the idempotent set. As a consequence, we obtain a new and simpler proof of the following theorem of Shneperman: a compact inverse semigroup has enough finite dimensional irreducible representations to separate points if and only if its idempotent set is totally disconnected. Our last theorem is the following: every norm continuous irreducible ∗-representation of a compact inverse semigroup on a Hilbert space is finite dimensional.
Date: 2011
URI: http://hdl.handle.net/10393/20183
Supervisor: Handelman David
Steinberg, Benjamin
Faculty: Sciences / Science
Degree: PhD

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