Speaker: Yosuke Kubota (Riken)
Title: Reconstruction of the Bost-Connes groupoid from K-theoretic data
Time/Date: 4:45-6:15, Monday, April 10, 2017.
Abstract: The Bost-Connes system is a C*-dynamical system (or often said to be a quantum statistical mechanics) attached to a number field, which realizes the arithmetics of the number field through its dynamics. It is first defined by Bost-Connes for the rational number field and generalized for an arbitrary number field after 15-year effort by many mathematicians. For the definition, one starts with a groupoid and consider a restriction of the "dual action" on its convolution C*-algebra. In this talk, we show that the Bost-Connes groupoids attached to two number fields are isomorphic if and only if their convolution C*-algebra have the same K-theoretic data. For the proof, we directly reconstruct the groupoid from their K-groups. This is a joint work with Takuya Takeishi.