Classification of actions of discrete Kac algebras on injective factors

Toshihiko Masuda, Reiji Tomatsu

Research output: Contribution to journalReview article

2 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 languageEnglish
Pages (from-to)1-134
Number of pages134
JournalMemoirs of the American Mathematical Society
Volume245
Issue number1160
DOIs
Publication statusPublished - Jan 1 2017

Fingerprint

Injective
Towers
Algebra
Invariant
Free Action
Centralizer
Discrete Group
Group Action
Module
Generalise

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

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

In: Memoirs of the American Mathematical Society, Vol. 245, No. 1160, 01.01.2017, p. 1-134.

Research output: Contribution to journalReview article

@article{15235df0dd2e41b5adca02b8269caa4a,
title = "Classification of actions of discrete Kac algebras on injective factors",
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.",
author = "Toshihiko Masuda and Reiji Tomatsu",
year = "2017",
month = "1",
day = "1",
doi = "10.1090/memo/1160",
language = "English",
volume = "245",
pages = "1--134",
journal = "Memoirs of the American Mathematical Society",
issn = "0065-9266",
publisher = "American Mathematical Society",
number = "1160",

}

TY - JOUR

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

AU - Masuda, Toshihiko

AU - Tomatsu, Reiji

PY - 2017/1/1

Y1 - 2017/1/1

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

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 -