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

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dc.contributor.authorWiart, Jaspar
dc.contributor.supervisorLaca, Marcelo
dc.contributor.supervisorTrifkovic, Mak
dc.date.accessioned2013-08-15T22:55:08Z
dc.date.available2013-08-15T22:55:08Z
dc.date.copyright2013en_US
dc.date.issued2013-08-15
dc.degree.departmentDepartment of Mathematics and Statistics
dc.degree.levelMaster of Science M.Sc.en_US
dc.description.abstractIn 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].en_US
dc.description.proquestcode0405en_US
dc.description.proquestemailjaspar.wiart@gmail.comen_US
dc.description.scholarlevelGraduateen_US
dc.identifier.urihttp://hdl.handle.net/1828/4750
dc.languageEnglisheng
dc.language.isoenen_US
dc.rights.tempAvailable to the World Wide Weben_US
dc.subjectToeplitz Algebraen_US
dc.subjectSemigroupen_US
dc.subjectNumber Ringen_US
dc.subjectUniversal C*-algebraen_US
dc.subjectIsometriesen_US
dc.subjectC*-algebras generated by isometriesen_US
dc.subjectFaithful Representationen_US
dc.titleA characterization of faithful representations of the Toeplitz algebra of the ax+b-semigroup of a number ringen_US
dc.typeThesisen_US

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