Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Engineering
A Residue Formula For The Fundamental Hochschild 3-Cocycle For Suq(2), Ulrich Krahmer, Adam Rennie, Roger Senior
A Residue Formula For The Fundamental Hochschild 3-Cocycle For Suq(2), Ulrich Krahmer, Adam Rennie, Roger Senior
Associate Professor Adam Rennie
An analogue of a spectral triple over SUq(2) is constructed for which the usual assumption of bounded commutators with the Dirac operator fails. An analytic expression analogous to that for the Hochschild class of the Chern character for spectral triples yields a non-trivial twisted Hochschild 3-cocycle. The problems arising from the unbounded commutators are overcome by defining a residue functional using projections to cut down the Hilbert space.
The Local Index Formula In Noncommutative Geometry Revisited, Alan Carey, John Phillips, Adam Rennie, Fyodor Sukochev
The Local Index Formula In Noncommutative Geometry Revisited, Alan Carey, John Phillips, Adam Rennie, Fyodor Sukochev
Associate Professor Adam Rennie
In this review we discuss the local index formula in noncommutative geomety from the viewpoint of two new proofs are partly inspired by the approach of Higson especially that in but they differ in several fundamental aspedcts, in particular they apply to semifinite spectral triples for a *s-subalgebra A of a general semifinite von Neumann algebra. Our proofs are novel even in the setting of the original theorem and reduce the hypotheses of the theorem to those necessary for its statement. These proofs rely on the introduction of a function valued cocycle which is 'almost' a (b, B)-cocycle in the …