TY - JOUR

T1 - Twisted cyclic theory, equivariant KK-theory and KMS states

AU - Carey, Alan L.

AU - Neshveyev, Sergey

AU - Nest, Ryszard

AU - Rennie, Adam

PY - 2011/1

Y1 - 2011/1

N2 - Given a C*-algebra A with a KMS weight for a circle action, we construct and compute a secondary invariant on the equivariant K-theory of the mapping cone of , both in terms of equivariant KK-theory and in terms of a semifinite spectral flow. This in particular puts the previously considered examples of Cuntz algebras [Carey, Phillips, Rennie, Twisted cyclic theory and the modular index theory of Cuntz algebras] and SUq(2) [Carey, Rennie, Tong, J. Geom. Phys. 59: 1431-1452, 2009] in a general framework. As a new example we consider the Araki-Woods IIIλ representations of the Fermion algebra.

AB - Given a C*-algebra A with a KMS weight for a circle action, we construct and compute a secondary invariant on the equivariant K-theory of the mapping cone of , both in terms of equivariant KK-theory and in terms of a semifinite spectral flow. This in particular puts the previously considered examples of Cuntz algebras [Carey, Phillips, Rennie, Twisted cyclic theory and the modular index theory of Cuntz algebras] and SUq(2) [Carey, Rennie, Tong, J. Geom. Phys. 59: 1431-1452, 2009] in a general framework. As a new example we consider the Araki-Woods IIIλ representations of the Fermion algebra.

UR - http://www.scopus.com/inward/record.url?scp=79551637145&partnerID=8YFLogxK

U2 - 10.1515/CRELLE.2011.007

DO - 10.1515/CRELLE.2011.007

M3 - Article

SN - 0075-4102

SP - 161

EP - 191

JO - Journal fur die Reine und Angewandte Mathematik

JF - Journal fur die Reine und Angewandte Mathematik

IS - 650

ER -