Strong solidity of group factors from lattices in SO(n,1) and SU(n,1)
By Thomas Sinclair. 2010
59 citations recorded by the source corpus.
Abstract We show that the group factors LΓ, where Γ is an ICC lattice in either SO ( n , 1 ) or SU ( n , 1 ) , n ⩾ 2 , are strongly solid in the sense of Ozawa and Popa (2010) [13] . This strengthens a result of Ozawa and Popa (2010) [14] showing that these factors do not have Cartan subalgebras.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/66de8f328d759de311d2f2211578bd315f8eb105
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In Algebra and Number Theory
- Adrian Ioana
- I. Chifan
- Bogdan Udrea
- Thomas Sinclair
- S. Vaes
- Sorin Popa
- Cyril Houdayer
- Mihaita Berbec
In Mathematical Physics
- Adrian Ioana
- I. Chifan
- Thomas Sinclair
- Bogdan Udrea
- S. Vaes
- Sorin Popa
- Cyril Houdayer
- Mihaita Berbec
Citations in the corpus
- Classification and rigidity for von Neumann algebras (2012, background): “ith2))|M 2 . See also [Po86, Po06c] for the construction of a malleable deformation for the free group factors. Example 3.6. Next, we recall the construction of a malleable deformation from cocycles ([Si10], see also [PS09]). Start with a countable group Γ, an orthogonal representation π : Γ →O(H) o”
- RIGIDITY FOR VON NEUMANN ALGEBRAS (2017, result): “In a complementary direction, it was recently shown in Chifan, de Santiago, and Sinclair [2016] that for a wide family of product groupsΓ, the von Neumann algebra L(Γ) completely remembers the product structure of Γ.”
- ON THE STRUCTURAL THEORY OF II1 FACTORS OF NEGATIVELY CURVED GROUPS, II. ACTIONS BY PRODUCT GROUPS (2011, methodology): “Using similar computations as in [30, 39] one can verify that we have the following properties: Pʀɪɪɴ 2.”