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Full-Text Articles in Science and Technology Studies
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.
Families Of Type Iii Kms States On A Class Of C-Algebras Containing On And Qn, A L. Carey, J Phillips, I F. Putnam, A Rennie
Families Of Type Iii Kms States On A Class Of C-Algebras Containing On And Qn, A L. Carey, J Phillips, I F. Putnam, A Rennie
Associate Professor Adam Rennie
We construct a family of purely infinite C¤-algebras, Q¸ for ¸ 2 (0, 1) that are classified by their K-groups. There is an action of the circle T with a unique KMS state à on each Q¸. For ¸ = 1/n, Q1/n »= On, with its usual T action and KMS state. For ¸ = p/q, rational in lowest terms, Q¸ »= On (n = q − p + 1) with UHF fixed point algebra of type (pq)1. For any n > 1, Q¸ »= On for infinitely many ¸ with distinct KMS states and UHF fixed-point algebras. For any ¸ …