Co-rigidity of groups, von Neumann algebras and Kac algebras
- Authors
- Heo, Jaeseong
- Issue Date
- Dec-2007
- Publisher
- WILEY-V C H VERLAG GMBH
- Keywords
- property T; relative property T; co-rigidity; II1-factor; Kac algebra
- Citation
- MATHEMATISCHE NACHRICHTEN, v.280, no.1-2, pp.83 - 92
- Indexed
- SCIE
SCOPUS
- Journal Title
- MATHEMATISCHE NACHRICHTEN
- Volume
- 280
- Number
- 1-2
- Start Page
- 83
- End Page
- 92
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/179228
- DOI
- 10.1002/mana.200410466
- ISSN
- 0025-584X
- 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.
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