### 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 |
---|---|

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 - 2017 Jan |

### Keywords

- Action
- Discrete Kac algebra
- Von Neumann algebra

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

## Fingerprint Dive into the research topics of 'Classification of actions of discrete Kac algebras on injective factors'. Together they form a unique fingerprint.

## Cite this

Masuda, T., & Tomatsu, R. (2017). Classification of actions of discrete Kac algebras on injective factors.

*Memoirs of the American Mathematical Society*,*245*(1160), 1-134. https://doi.org/10.1090/memo/1160