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

Format:

Book

Author/Creator:

Masuda, Toshihiko, author.

Tomatsu, Reiji, 1978- author.

Series:

Memoirs of the American Mathematical Society ; Volume 245, Number 1160 (fifth of 6 numbers)

Memoirs of the American Mathematical Society, 1947-6221 ; Volume 245, Number 1160 (fifth of 6 numbers)

Language:

English

Subjects (All):

Kac-Moody algebras.

Lie algebras.

Injective modules (Algebra).

Physical Description:

1 online resource (134 pages) : illustrations.

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2017.

Summary:

The authors study two kinds of actions of a discrete amenable Kac algebra. The first one is an action whose modular part is normal. They 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, the authors show that the Connes-Takesaki module is a complete invariant.

Contents:

Preliminary

Canonical extension of irreducible endomorphisms

Kac alebras

Classification of modular kernels

Classification of actions with non-trivial modular parts

Classification of centrally free actions

Related problems.

Notes:

Includes bibliographical references and index.

Description based on print version record.

"Volume 245, number 1160 (fifth of 6 numbers), January 2017."

ISBN:

1-4704-3609-4