Journal of Operator Theory

Volume 60, Issue 2, Fall 2008 pp. 273-300.

Classification of actions of duals of finite groups on the AFD factor of type II$_1$

Authors: Toshihiko Masuda
Author institution: Graduate School of Mathematics, Kyushu University, 6-10-1 Hakozaki, Fukuoka, 812-8581, Japan

Summary: We will show the uniqueness of outer coactions of finite groups on the AFD factor of type II$_1$ along the arguments by Connes, Jones and Ocneanu. Namely, we construct the infinite tensor product type action, adopt it as the model action, and prove that any outer coaction is conjugate to the model action.

Keywords: Coaction, action of group dual, cohomology vanishing, model action splitting.

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