Fixed point property for universal lattice on Schatten classes

Details Fixed point property for universal lattice on Schatten classes Fixed point property for universal lattice on Schatten classes

2010-10-21

arxiv.org/abs/1010.4532v2

Mathematics

Group Theory

14 pages, some gap in the previous version (on heredity to lattices) fixed, and some explanation added; 10 pages, no figures

Scientific paper

The special linear group G=SL_n(Z[x1,...,xk]) (n at least 3 and k finite) is called the universal lattice. Let n be at least 4, p be any real number in (1,\infty). 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 generalization of previous theorems repsectively of the author and of Bader--Furman--Gelander--Monod, which treated commutative Lp-setting.

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