KMS states on the crossed product C*-algebra of a homeomorphism

Johannes Christensen (Aarhus University)

Thursday 5th December, 2019 16:00-17:00 Maths 311B


Since its introduction, the theory of operator algebras has been interacting closely with the theory of dynamical systems. A classical way to associate a C*-algebra to a dynamical system is via the crossed product C*-algebra of a homeomorphism. If a homeomorphism acts on a compact metric space X, one can construct a one-parameter group for each real-valued continuous function F on X by “twisting” the unitary. 

In this talk I will analyse the KMS states for the one-parameter groups arising from such continuous functions by developing an intimate relation to the ergodic theory of non-singular transformations. I will show that the structure of KMS-states can be very rich and complicated. The results I will present in this talk is joint work with Klaus Thomsen.

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