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2012•arXiv (Cornell University)Open access

Rohlin flows on von Neumann algebras

Toshihiko Masuda, Reiji Tomatsu

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Abstract

We will introduce the Rohlin property for flows on von Neumann algebras and classify them up to strong cocycle conjugacy. This result provides alternative approaches to some preceding results such as Kawahigashi's classification of flows on the injective type II$_1$ factor, the classification of injective type III factors due to Connes, Krieger and Haagerup and the non-fullness of type III$_0$ factors. Several concrete examples are also studied.

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We will introduce the Rohlin property for flows on von Neumann algebras and classify them up to strong cocycle conjugacy. This result provides alternative approaches to some preceding results such as Kawahigashi's classification of flows on the injective type II$_1$ factor, the classification of injective type III factors due to Connes, Krieger and Haagerup and the non-fullness of type III$_0$ factors. Several concrete examples are also studied.

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Available abstract

We will introduce the Rohlin property for flows on von Neumann algebras and classify them up to strong cocycle conjugacy. This result provides alternative approaches to some preceding results such as Kawahigashi's classification of flows on the injective type II$_1$ factor, the classification of injective type III factors due to Connes, Krieger and Haagerup and the non-fullness of type III$_0$ factors. Several concrete examples are also studied.

Key concepts: Von Neumann architecture, Injective function, Property (philosophy), Pure mathematics, Type (biology), Mathematics, Von Neumann algebra, Conjugacy class

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