### Abstract

We show the uniqueness of minimal actions of a compact Kac algebra with amenable dual on the AFD factor of type II_{1}. 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.

Original language | English |
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Pages (from-to) | 487-551 |

Number of pages | 65 |

Journal | Communications in Mathematical Physics |

Volume | 274 |

Issue number | 2 |

DOIs | |

Publication status | Published - Sep 1 2007 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*,

*274*(2), 487-551. https://doi.org/10.1007/s00220-007-0269-4

**Classification of minimal actions of a compact kac algebra with amenable dual.** / Masuda, Toshihiko; Tomatsu, Reiji.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 274, no. 2, pp. 487-551. https://doi.org/10.1007/s00220-007-0269-4

}

TY - JOUR

T1 - Classification of minimal actions of a compact kac algebra with amenable dual

AU - Masuda, Toshihiko

AU - Tomatsu, Reiji

PY - 2007/9/1

Y1 - 2007/9/1

N2 - 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.

AB - 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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UR - http://www.scopus.com/inward/citedby.url?scp=34547185950&partnerID=8YFLogxK

U2 - 10.1007/s00220-007-0269-4

DO - 10.1007/s00220-007-0269-4

M3 - Article

AN - SCOPUS:34547185950

VL - 274

SP - 487

EP - 551

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -