Journal article
Superrigidity for dense subgroups of lie groups and their actions on homogeneous spaces
Mathematische annalen, Vol.386(3-4), pp.2015-2059
08/01/2023
DOI: 10.1007/s00208-022-02437-1
Abstract
An essentially free group action Gamma curved right arrow (X, mu) is called W*-supeffigid if the crossed product von Neumann algebra L-infinity (X) x Gamma completely remembers the group Gamma and its action on (X, mu). We prove W*-superrigidity for a class of infinite measure preserving actions, in particular for natural dense subgroups of isometries of the hyperbolic plane. The main tool is a new cocycle superrigidity theorem for dense subgroups of Lie groups acting by translation. We also provide numerous countable type II1 equivalence relations that cannot be implemented by an essentially free action of a group, both of geometric nature and through a wreath product construction.
Details
- Title: Subtitle
- Superrigidity for dense subgroups of lie groups and their actions on homogeneous spaces
- Creators
- Daniel Drimbe - KU LeuvenStefaan Vaes - KU Leuven
- Resource Type
- Journal article
- Publication Details
- Mathematische annalen, Vol.386(3-4), pp.2015-2059
- DOI
- 10.1007/s00208-022-02437-1
- ISSN
- 0025-5831
- eISSN
- 1432-1807
- Publisher
- Springer Nature
- Number of pages
- 45
- Grant note
- G090420N / FWO research project of the Research Foundation Flanders; FWO Flemish Government 12T5221N / Research Foundation-Flanders; FWO
- Language
- English
- Date published
- 08/01/2023
- Academic Unit
- Mathematics
- Record Identifier
- 9984696757102771
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