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arXiv · 1306.5046

Classification of actions of discrete Kac algebras on injective factors

Toshihiko Masuda·Reiji Tomatsu
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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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Toshihiko Masuda, Reiji Tomatsu. 2013-06-21. Classification of actions of discrete Kac algebras on injective factors. https://arxiv.org/abs/1306.5046

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