TY - JOUR
T1 - Fixed point property for universal lattice on schatten classes
AU - Mimura, Masato
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
KW - Bounded cohomology
KW - Fixed point property
KW - Kazhdan's property (T)
KW - Noncommutative L -spaces
KW - Schatten class operators
UR - http://www.scopus.com/inward/record.url?scp=84868136538&partnerID=8YFLogxK
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U2 - 10.1090/S0002-9939-2012-11711-3
DO - 10.1090/S0002-9939-2012-11711-3
M3 - Article
AN - SCOPUS:84868136538
SN - 0002-9939
VL - 141
SP - 65
EP - 81
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 1
ER -