Schatten类上泛格的不动点性质
Fixed point property for universal lattice on Schatten classes
摘要：
特殊线性群G=SL_n（Z[x1，...，xk]）（n至少为3且k有限）称为泛格。设n至少为4，p为（1，\infty）中的任意实数。主要结果是：G的任意有限指数子群关于p-Schatten类算子空间上的仿射等距作用具有不动点性质.此外，还证明了高阶格也具有同样的性质。这些结果是作者和Bader-Furman-Gelander-Monod关于交换Lp-集的定理的推广。
英文摘要：
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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