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Classification of Minimal Actions of a Compact Kac Algebra with Amenable Dual

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Abstract

We show the uniqueness of minimal actions of a compact Kac algebra with amenable dual on the AFD factor of type II1. This particularly implies the uniqueness of minimal actions of a compact group. Our main tools are a Rohlin type theorem, the 2-cohomology vanishing theorem, and the Evans-Kishimoto type intertwining argument.

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Authors and Affiliations

  1. Graduate School of Mathematics, Kyushu University, 6-10-1 Hakozaki, Fukuoka, 812-8581, Japan

    Toshihiko Masuda

  2. Department of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, 153-8914, Japan

    Reiji Tomatsu

Authors
  1. Toshihiko Masuda
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  2. Reiji Tomatsu
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Correspondence to Toshihiko Masuda.

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Communicated by Y. Kawahigashi

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Masuda, T., Tomatsu, R. Classification of Minimal Actions of a Compact Kac Algebra with Amenable Dual. Commun. Math. Phys. 274, 487–551 (2007). https://doi.org/10.1007/s00220-007-0269-4

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  • DOI: https://doi.org/10.1007/s00220-007-0269-4

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