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

• Main Author: Wiart, Jaspar
• Other Authors: Laca, Marcelo
• Language: English; en
• Published: 2013
• Subjects: Toeplitz Algebra; Semigroup; Number Ring; Universal C*-algebra; Isometries; C*-algebras generated by isometries; Faithful Representation
• Online Access: http://hdl.handle.net/1828/4750

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 === [e-mail]