  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.

Group Theory;Operator Algebras