### Abstract

We will study two kinds of actions of a discrete amenable Kac algebra. The first one is an action whose modular part is normal. We will construct a new invariant which generalizes a characteristic invariant for a discrete group action, and we will present a complete classification. The second is a centrally free action. By constructing a Rohlin tower in an asymptotic centralizer, we will show that the Connes-Takesaki module is a complete invariant.

Original language | English |
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Pages (from-to) | 1-134 |

Number of pages | 134 |

Journal | Memoirs of the American Mathematical Society |

Volume | 245 |

Issue number | 1160 |

DOIs | |

Publication status | Published - Jan 2017 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

*Memoirs of the American Mathematical Society*,

*245*(1160), 1-134. https://doi.org/10.1090/memo/1160

**Classification of actions of discrete Kac algebras on injective factors.** / Masuda, Toshihiko; Tomatsu, Reiji.

Research output: Contribution to journal › Review article

*Memoirs of the American Mathematical Society*, vol. 245, no. 1160, pp. 1-134. https://doi.org/10.1090/memo/1160

}

TY - JOUR

T1 - Classification of actions of discrete Kac algebras on injective factors

AU - Masuda, Toshihiko

AU - Tomatsu, Reiji

PY - 2017/1

Y1 - 2017/1

N2 - We will study two kinds of actions of a discrete amenable Kac algebra. The first one is an action whose modular part is normal. We will construct a new invariant which generalizes a characteristic invariant for a discrete group action, and we will present a complete classification. The second is a centrally free action. By constructing a Rohlin tower in an asymptotic centralizer, we will show that the Connes-Takesaki module is a complete invariant.

AB - We will study two kinds of actions of a discrete amenable Kac algebra. The first one is an action whose modular part is normal. We will construct a new invariant which generalizes a characteristic invariant for a discrete group action, and we will present a complete classification. The second is a centrally free action. By constructing a Rohlin tower in an asymptotic centralizer, we will show that the Connes-Takesaki module is a complete invariant.

UR - http://www.scopus.com/inward/record.url?scp=85006049049&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85006049049&partnerID=8YFLogxK

U2 - 10.1090/memo/1160

DO - 10.1090/memo/1160

M3 - Review article

AN - SCOPUS:85006049049

VL - 245

SP - 1

EP - 134

JO - Memoirs of the American Mathematical Society

JF - Memoirs of the American Mathematical Society

SN - 0065-9266

IS - 1160

ER -