Modular spectral triples and KMS states in noncommutative geometry
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]
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