Journal article
Prime II1 factors arising from irreducible lattices in products of rank one simple Lie groups
Journal für die reine und angewandte Mathematik, Vol.757(757), pp.197-246
12/01/2019
DOI: 10.1515/crelle-2017-0039
Abstract
We prove that if Gamma is an icc irreducible lattice in a product of connected non-compact rank one simple Lie groups with finite center, then the II1 factor L(Gamma) is prime. In particular, we deduce that the II1 factors associated to the arithmetic groups PSL2(Z[root d]) and PSL2(Z[S-1]) are prime for any square-free integer d >= 2 with d not equivalent to 1 (mod 4) and any finite non-empty set of primes S. This provides the first examples of prime II1 factors arising from lattices in higher rank semisimple Lie groups. More generally, we describe all tensor product decompositions of L(Gamma) for icc countable groups Gamma that are measure equivalent to a product of non-elementary hyperbolic groups. In particular, we show that L(Gamma) is prime, unless Gamma is a product of infinite groups, in which case we prove a unique prime factorization result for L(Gamma).
Details
- Title: Subtitle
- Prime II1 factors arising from irreducible lattices in products of rank one simple Lie groups
- Creators
- Daniel Drimbe - University of California, San DiegoDaniel Hoff - University of California, Los AngelesAdrian Ioana - University of California, San Diego
- Resource Type
- Journal article
- Publication Details
- Journal für die reine und angewandte Mathematik, Vol.757(757), pp.197-246
- Publisher
- Walter De Gruyter
- DOI
- 10.1515/crelle-2017-0039
- ISSN
- 0075-4102
- eISSN
- 1435-5345
- Number of pages
- 50
- Grant note
- 1144086 / NSF GRFP Grant DGE Alfred. P. Sloan Foundation Fellowship; Alfred P. Sloan Foundation 1344970 / NSF RTG DMS; National Science Foundation (NSF); NSF - Directorate for Mathematical & Physical Sciences (MPS) 1253402 / NSF Career Grant DMS
- Language
- English
- Date published
- 12/01/2019
- Academic Unit
- Mathematics
- Record Identifier
- 9984696758402771
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