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Full-Text Articles in Science and Technology Studies
The Chern Character Of Semifinite Spectral Triples, Alan L. Carey, John Phillips, Adam C. Rennie, Fyodor A. Sukochev
The Chern Character Of Semifinite Spectral Triples, Alan L. Carey, John Phillips, Adam C. Rennie, Fyodor A. Sukochev
Faculty of Engineering and Information Sciences - Papers: Part A
In previous work we generalised both the odd and even local index formula of Connes and Moscovici to the case of spectral triples for a ∗-subalgebra A of a general semifinite von Neumann algebra. Our proofs are novel even in the setting of the original theorem and rely on the introduction of a function valued cocycle (called the resolvent cocycle) which is 'almost' a (b,B)-cocycle in the cyclic cohomology of A. In this paper we show that this resolvent cocycle 'almost' represents the Chern character, and assuming analytic continuation properties for zeta functions, we show that the associated residue cocycle, …
Semifinite Spectral Triples Associated With Graph C*-Algebras, Alan L. Carey, John Phillips, Adam Rennie
Semifinite Spectral Triples Associated With Graph C*-Algebras, Alan L. Carey, John Phillips, Adam Rennie
Faculty of Engineering and Information Sciences - Papers: Part A
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.