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KK-theory and spectral flow in von Neumann algebras

Kaad, J; Nest, Ryszard; Rennie, Adam

Description

We present a definition of spectral flow for any norm closed ideal J in any von Neumann algebra N. Given a path of selfadjoint operators in N which are invertible in N/J, the spectral flow produces a class in Ko (J). Given a semifinite spectral triple (A, H, D) relative to (N, τ) with A separable, we construct a class [D] ∈ KK1 (A, K(N)). For a unitary u ∈ A, the von Neumann spectral flow between D and u*Du is equal to the Kasparov product [u] A[D], and is simply related to the numerical...[Show more]

dc.contributor.authorKaad, J
dc.contributor.authorNest, Ryszard
dc.contributor.authorRennie, Adam
dc.date.accessioned2015-12-10T23:36:15Z
dc.identifier.issn1865-2433
dc.identifier.urihttp://hdl.handle.net/1885/70061
dc.description.abstractWe present a definition of spectral flow for any norm closed ideal J in any von Neumann algebra N. Given a path of selfadjoint operators in N which are invertible in N/J, the spectral flow produces a class in Ko (J). Given a semifinite spectral triple (A, H, D) relative to (N, τ) with A separable, we construct a class [D] ∈ KK1 (A, K(N)). For a unitary u ∈ A, the von Neumann spectral flow between D and u*Du is equal to the Kasparov product [u] A[D], and is simply related to the numerical spectral flow, and a refined C* -spectral flow.
dc.publisherCambridge University Press
dc.sourceJournal of K-Theory
dc.subjectKeywords: KK-theory; spectral flow; von Neumann algebra
dc.titleKK-theory and spectral flow in von Neumann algebras
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume10
dc.date.issued2012
local.identifier.absfor010108 - Operator Algebras and Functional Analysis
local.identifier.absfor010103 - Category Theory, K Theory, Homological Algebra
local.identifier.ariespublicationf5625xPUB2209
local.type.statusPublished Version
local.contributor.affiliationKaad, J, University of Copenhagen
local.contributor.affiliationNest, Ryszard, Copenhagen University
local.contributor.affiliationRennie, Adam, College of Physical and Mathematical Sciences, ANU
local.description.embargo2037-12-31
local.bibliographicCitation.issue2
local.bibliographicCitation.startpage241
local.bibliographicCitation.lastpage277
local.identifier.doi10.1017/is012003003jkt185
dc.date.updated2016-02-24T08:55:45Z
local.identifier.scopusID2-s2.0-84869191507
local.identifier.thomsonID000301175600006
CollectionsANU Research Publications

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