Operator Algebra Seminar

Speaker:  Takuya Takeishi (University of Tokyo)

Title: On the classification problem of Bost-Connes systems

Abstract : The classification problem of Bost-Connes systems was studied by Cornelissen and Marcolli, but still remains unsolved. For this problem, we generalize the result of Laca and Raeburn for the primitive ideal space of Bost-Connes systems for Q. As consequence, we can obtain the narrow class number of the field by looking at the dimension of finite dimensional irreducible representations. In particular, the narrow class number is an invariant of Bost Connes C*-algebras. Moreover, I will talk on recent progress of K-theoretic approach to the classification problem.