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A characterization of faithful representations of the Toeplitz algebra of the ax+b-semigroup of a number ring

In their paper [2] Cuntz, Deninger, and Laca introduced a C*-algebra \mathfrak{T}[R] associated to a number ring R and showed that it was functorial for injective ring homomorphisms and had an interesting KMS-state structure, which they computed directly. Although isomorphic to the Toeplitz algebra of the ax+b-semigroup R⋊R^× of R, their C*-algebra \mathfrak{T}[R] was defined in terms of relations on a generating set of isometries and projections. They showed that a homomorphism φ:\mathfrak{T}[R]→ A is injective if and only if φ is injective on a certain commutative *-subalgebra of \mathfrak{T}[R]. In this thesis we give a direct proof of this result, and go on to show that there is a countable collection of projections which detects injectivity, which allows us to simplify their characterization of faithful representations of \mathfrak{T}[R]. / Graduate / 0405 / jaspar.wiart@gmail.com

Identiferoai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/4750
Date15 August 2013
CreatorsWiart, Jaspar
ContributorsLaca, Marcelo, Trifkovic, Mak
Source SetsUniversity of Victoria
LanguageEnglish, English
Detected LanguageEnglish
TypeThesis
RightsAvailable to the World Wide Web

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