Abstract
The special linear group G = SL n(ℤ[x 1,..., x k]) (n at least 3 and k finite) is called the universal lattice. Let n be at least 4, and p be any real number in (1,∞). The main result is the following: any finite index subgroup of G has the fixed point property with respect to every affine isometric action on the space of p-Schatten class operators. It is in addition shown that higher rank lattices have the same property. These results are a generalization of previous theorems respectively of the author and of Bader-Furman-Gelander- Monod, which treated a commutative L p-setting.
Original language | English |
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Pages (from-to) | 65-81 |
Number of pages | 17 |
Journal | Proceedings of the American Mathematical Society |
Volume | 141 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2012 |
Externally published | Yes |
Keywords
- Bounded cohomology
- Fixed point property
- Kazhdan's property (T)
- Noncommutative L -spaces
- Schatten class operators
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics