Co-rigidity of groups, von Neumann algebras and Kac algebras

In this paper, we consider a generalization of property T of Kazhdan for groups and property T of Connes for von Neumann algebras. We introduce another relative property T for groups corresponding to co‐rigidity for von Neumann algebras, which is different from relative property T of Margulis. We in...

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Bibliographic Details
Published in:Mathematische Nachrichten 2007-01, Vol.280 (1-2), p.83-92
Main Author: Heo, Jaeseong
Format: Article
Language:English
Subjects:
co-rigidity
II1-factor
Kac algebra
Property T
relative property T
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Summary:In this paper, we consider a generalization of property T of Kazhdan for groups and property T of Connes for von Neumann algebras. We introduce another relative property T for groups corresponding to co‐rigidity for von Neumann algebras, which is different from relative property T of Margulis. We investigate the connection between a pair of von Neumann algebras and a pair of their commutants with respect to co‐rigidity. We define relative property T and co‐rigidity for a pair of Kac algebras as the generalizations of relative property T and co‐rigidity for groups. We show that the tensor product of two Kac algebras has property T if and only if two Kac algebras all have property T. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.200410466