KMS bundles of rationally AF algebras with finitely many parameters

Yasuhiko Sato  (Kyushu University)

8:15-9:15£¨August 2£¨2024    Tian Jiabing Building 323


We construct crossed products of certain non-simple rationally AF (RAF) algebras by the free groups, based on the study going back to Bratteli-Elliott-Kishimoto's method for actions of the free groups on AF algebras. In their construction of crossed products of free groups, the nuclearity can be implicitly obtained from the existence of approximate diagonal which is known to be equivalent with the nuclearity of C*-algebras, and our present construction heavily relies on their technique. As a consequence, our construction of crossed products of RAF algebras realizes any possible temperature state space with finitely many parameters on the Jiang-Su algebra, more generally on a unital separable simple nuclear Z-absorbing C*-algebra with a unique tracial state. This result is obtained as an application of the classification theory of non-simple RAF algebras, by following the recent classification strategy for simple nuclear C*-algebras.

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