Twisted cyclic theory, equivariant KK-theory and KMS states

TY - JOUR

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

AU - Carey, Alan

AU - Neshveyev, Sergey

AU - Nest, Ryszard

AU - Rennie, Adam Charles

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.

M3 - Journal article

SN - 0075-4102

VL - 650

SP - 161

EP - 191

JO - Journal fuer die Reine und Angewandte Mathematik

JF - Journal fuer die Reine und Angewandte Mathematik

ER -