We present some techniques in the construction of spectral triples for C*-algebras, in particular those which determine a compatible metric on the state space, which provides a noncommutative analogue of geodesic distance between points on a manifold. The main body of the thesis comprises three sections. In the first, we provide a further analysis on the existence of spectral triples on crossed products by discrete groups and their interplay with classical metric dynamics. Dynamical systems arising from non-unital C*-algebras and certain semidirect products of groups are considered. The second section is a construction of spectral triples for certain unital extensions by stable ideals, using the language of unbounded Kasparov theory as presented by Mesland, Kaad and others, These ideas can be implemented for both the equatorial Podle\'s spheres and quantum SU2 group. Finally, we investigate the potential of the construction of twisted spectral triples, as outlined by Connes and Moscovici. We achieve a construction of twisted spectral triples on all simple Cuntz-Krieger algebras, whose unique KMS state is obtained from the asymptotics of the Dirac.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:594648 |
| Date | January 2013 |
| Creators | Hawkins, Andrew |
| Publisher | University of Nottingham |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://eprints.nottingham.ac.uk/13506/ |
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