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Modular spectral triples and KMS states in noncommutative geometry

Senior, Roger John

Description

This thesis investigates the role of dimension in the noncommutative geometry of quantum groups and their homogeneous spaces. We define a generalisation of semifinite spectral triples called modular spectral triples, which replaces the trace with a weight. We prove a resolvent index formula, which computes the index pairing between modular spectral triples and equivariant K-theory. We demonstrate that a modular spectral triple for the Podles sphere has spectral and homological dimension 2....[Show more]

dc.contributor.authorSenior, Roger John
dc.date.accessioned2018-11-22T00:05:16Z
dc.date.available2018-11-22T00:05:16Z
dc.date.copyright2011
dc.identifier.otherb2638815
dc.identifier.urihttp://hdl.handle.net/1885/150250
dc.description.abstractThis thesis investigates the role of dimension in the noncommutative geometry of quantum groups and their homogeneous spaces. We define a generalisation of semifinite spectral triples called modular spectral triples, which replaces the trace with a weight. We prove a resolvent index formula, which computes the index pairing between modular spectral triples and equivariant K-theory. We demonstrate that a modular spectral triple for the Podles sphere has spectral and homological dimension 2. We construct an analogue of a modular spectral triple over quantum SU(2) for which the assumption of bounded commutators fails. We construct a non-trivial twisted Hochschild 3-cocycle for quantum SU(2) using an analytic expression analogous to the Hochschild class of the Chern character for spectral triples. This construction gives the analogous spectral and homological dimension of 3 for quantum SU(2).
dc.format.extentx, 149 leaves.
dc.language.isoen_AU
dc.rightsAuthor retains copyright
dc.subject.lccQC20.7.D52 S46 2011
dc.subject.lcshNoncommutative differential geometry
dc.subject.lcshQuantum groups
dc.titleModular spectral triples and KMS states in noncommutative geometry
dc.typeThesis (PhD)
local.description.notesThesis (Ph.D.)--Australian National University
dc.date.issued2011
local.type.statusAccepted Version
local.contributor.affiliationAustralian National University. Dept. of Mathematics
local.identifier.doi10.25911/5d611b35c7897
dc.date.updated2018-11-20T06:05:05Z
dcterms.accessRightsOpen Access
local.mintdoimint
CollectionsOpen Access Theses

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