Classification of actions of discrete Kac algebras on injective factors

Toshihiko Masuda; Reiji Tomatsu

doi:10.1090/memo/1160

Classification of actions of discrete Kac algebras on injective factors

Toshihiko Masuda, Reiji Tomatsu

Research output: Contribution to journal › Review article › peer-review

6 Citations (Scopus)

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	https://doi.org/10.1090/memo/1160
Publication status	Published - 2017 Jan
Externally published	Yes

Keywords

Action
Discrete Kac algebra
Von Neumann algebra

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/memo/1160

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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.",

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author = "Toshihiko Masuda and Reiji Tomatsu",

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AU - Masuda, Toshihiko

AU - Tomatsu, Reiji

N1 - Publisher Copyright: © 2016 American Mathematical Society. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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.

KW - Action

KW - Discrete Kac algebra

KW - Von Neumann algebra

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DO - 10.1090/memo/1160

M3 - Review article

AN - SCOPUS:85006049049

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VL - 245

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EP - 134

JO - Memoirs of the American Mathematical Society

JF - Memoirs of the American Mathematical Society

IS - 1160

ER -

Classification of actions of discrete Kac algebras on injective factors

Abstract

Keywords

ASJC Scopus subject areas

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