Co‐rigidity of groups, von Neumann algebras and Kac algebras | Zendy

Heo Jaeseong | Zendy

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

Author(s) -

Heo Jaeseong

Publication year - 2007

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200410466

Subject(s) - mathematics , rigidity (electromagnetism) , von neumann architecture , crossed product , pure mathematics , abelian von neumann algebra , property (philosophy) , affiliated operator , jordan algebra , connection (principal bundle) , generalization , tensor product , combinatorics , algebra over a field , mathematical analysis , algebra representation , physics , geometry , quantum mechanics , philosophy , epistemology

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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