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Semifinite spectral triples associated with graph C∗-algebras

Chapter


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Abstract


  • We review the recent construction of semifinite spectral triples for graph C^*-algebras. These examples have inspired many other developments and we review some of these such as the relation between the semifinite index and the Kasparov product, examples of noncommutative manifolds, and an index theorem in twisted cyclic theory using a KMS state.

Publication Date


  • 2008

Citation


  • Carey, A. L., Phillips, J. & Rennie, A. (2008). Semifinite spectral triples associated with graph C∗-algebras. Traces in Number Theory, Geometry and Quantum Fields (Aspects of Mathematics) (pp. 35-56). Wiesbaden: Vieweg.

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1746&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/740

Book Title


  • Traces in Number Theory, Geometry and Quantum Fields (Aspects of Mathematics)

Start Page


  • 35

End Page


  • 56

Abstract


  • We review the recent construction of semifinite spectral triples for graph C^*-algebras. These examples have inspired many other developments and we review some of these such as the relation between the semifinite index and the Kasparov product, examples of noncommutative manifolds, and an index theorem in twisted cyclic theory using a KMS state.

Publication Date


  • 2008

Citation


  • Carey, A. L., Phillips, J. & Rennie, A. (2008). Semifinite spectral triples associated with graph C∗-algebras. Traces in Number Theory, Geometry and Quantum Fields (Aspects of Mathematics) (pp. 35-56). Wiesbaden: Vieweg.

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1746&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/740

Book Title


  • Traces in Number Theory, Geometry and Quantum Fields (Aspects of Mathematics)

Start Page


  • 35

End Page


  • 56