Fixed point property for universal lattice on schatten classes

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2 Citations (Scopus)


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 languageEnglish
Pages (from-to)65-81
Number of pages17
JournalProceedings of the American Mathematical Society
Issue number1
Publication statusPublished - 2012


  • Bounded cohomology
  • Fixed point property
  • Kazhdan's property (T)
  • Noncommutative L -spaces
  • Schatten class operators


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