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Articles 1 - 3 of 3
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.