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Full-Text Articles in Social and Behavioral Sciences
Twisted Cyclic Cohomology And Modular Fredholm Modules, Adam Rennie, Andrzej Sitarz, Makoto Yamashita
Twisted Cyclic Cohomology And Modular Fredholm Modules, Adam Rennie, Andrzej Sitarz, Makoto Yamashita
Associate Professor Adam Rennie
Connes and Cuntz showed in [Comm. Math. Phys. 114 (1988), 515-526] that suitable cyclic cocycles can be represented as Chern characters of finitely summable semifinite Fredholm modules. We show an analogous result in twisted cyclic cohomology using Chern characters of modular Fredholm modules. We present examples of modular Fredholm modules arising from Podles sphereś and from SUq (2).
Spectral Flow Invariants And Twisted Cyclic Theory For The Haar State On Suq(2), A L. Carey, A Rennie, K Tong
Spectral Flow Invariants And Twisted Cyclic Theory For The Haar State On Suq(2), A L. Carey, A Rennie, K Tong
Associate Professor Adam Rennie
In [A.L. Carey, J. Phillips, A. Rennie, Twisted cyclic theory and an index theory for the gauge invariant KMS state on Cuntz algebras. arXiv:0801.4605], we presented a K-theoretic approach to finding invariants of algebras with no non-trivial traces. This paper presents a new example that is more typical of the generic situation. This is the case of an algebra that admits only non-faithful traces, namely SUq.2/ and also KMS states. Our main results are index theorems (which calculate spectral flow), one using ordinary cyclic cohomology and the other using twisted cyclic cohomology, where the twisting comes from the generator of …
Twisted Cyclic Theory, Equivariant Kk-Theory And Kms States, Alan L. Carey, Sergey Neshveyev, R Nest, Adam Rennie
Twisted Cyclic Theory, Equivariant Kk-Theory And Kms States, Alan L. Carey, Sergey Neshveyev, R Nest, Adam Rennie
Associate Professor Adam Rennie
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 AT ,! A, 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 [10] and SUqð2Þ [14] in a general framework. As a new example we consider the Araki-Woods IIIl representations of the Fermion algebra.