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Classification of actions of discrete Kac algebras on injective factors
About this Title
Toshihiko Masuda, Graduate School of Mathematics, Kyushu University, Fukuoka, 819-0395 , Japan Department of Mathematics, Hokkaido University, Hokkaido 060-0810 , Japan
Publication: Memoirs of the American Mathematical Society
Publication Year:
2017; Volume 245, Number 1160
ISBNs: 978-1-4704-2055-0 (print); 978-1-4704-3609-4 (online)
DOI: https://doi.org/10.1090/memo/1160
Published electronically: July 26, 2016
Keywords: von Neumann algebra,
discrete Kac algebra,
action
MSC: Primary 46L65; Secondary 46L55
Table of Contents
Chapters
- Introduction
- 1. Preliminary
- 2. Canonical extension of irreducible endomorphisms
- 3. Kac algebras
- 4. Classification of modular kernels
- 5. Classification of actions with non-trivial modular parts
- 6. Classification of centrally free actions
- 7. Related problems
- 8. Appendix
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.- Hiroshi Ando and Uffe Haagerup, Ultraproducts of von Neumann algebras, J. Funct. Anal. 266 (2014), no. 12, 6842–6913. MR 3198856, DOI 10.1016/j.jfa.2014.03.013
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