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Title:
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Representation Theory of Compact Inverse Semigroups |
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Author:
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Hajji, Wadii |
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Abstract:
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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. |
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Date:
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2011 |
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URI:
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http://hdl.handle.net/10393/20183
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Supervisor:
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Handelman David
Steinberg, Benjamin |
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Faculty:
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Sciences / Science |
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Degree:
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PhD |
