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

✍ Scribed by Jaeseong Heo

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
167 KB
Volume
280
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

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)

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