Open Access. Powered by Scholars. Published by Universities.®
Science and Technology Studies Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
Articles 1 - 5 of 5
Full-Text Articles in Science and Technology Studies
Index Theory For Locally Compact Noncommutative Geometries, Alan Carey, V Gayral, Adam Rennie, F Sukochev
Index Theory For Locally Compact Noncommutative Geometries, Alan Carey, V Gayral, Adam Rennie, F Sukochev
Associate Professor Adam Rennie
Spectral triples for nonunital algebras model locally compact spaces in noncommutative geometry. In the present text, we prove the local index formula for spectral triples over nonunital algebras, without the assumption of local units in our algebra.
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.
Dense Domains, Symmetric Operators And Spectral Triples, Iain Forsyth, B Mesland, Adam Rennie
Dense Domains, Symmetric Operators And Spectral Triples, Iain Forsyth, B Mesland, Adam Rennie
Associate Professor Adam Rennie
This article is about erroneous attempts to weaken the standard definition of unbounded Kasparov module (or spectral triple). This issue has been addressed previously, but here we present concrete counterexamples to claims in the literature that Fredholm modules can be obtained from these weaker variations of spectral triple. Our counterexamples are constructed using self-adjoint extensions of symmetric operators.
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 …
An Analytic Approach To Spectral Flow In Von Neumann Algebras, M-T Benameur, Alan Carey, John Phillips, Adam Rennie, Fyodor Sukochev, K Wojciechowski
An Analytic Approach To Spectral Flow In Von Neumann Algebras, M-T Benameur, Alan Carey, John Phillips, Adam Rennie, Fyodor Sukochev, K Wojciechowski
Associate Professor Adam Rennie
The analytic approach to spectral flow is about ten years old. In that time it has evolved to cover an ever wider range of examples. The most critical extension was to replace Fredholm operators in the classical sense by Breuer-Fredholm operators in a semifinite von Neumann algebra. The latter have continuous spectrum so that the notion of spectral flow turns out to be rather more difficult to deal with. However quite remarkably there is a uniform approach in which the proofs do not depend on discreteness of the spectrum of the operators in question. The first part of this paper …