Approximation properties of simple Lie groups made discrete
Group Theory
2016-09-19 v2 Operator Algebras
Abstract
In this paper we consider the class of connected simple Lie groups equipped with the discrete topology. We show that within this class of groups the following approximation properties are equivalent: (1) the Haagerup property; (2) weak amenability; (3) the weak Haagerup property. In order to obtain the above result we prove that the discrete group GL(2,K) is weakly amenable with constant 1 for any field K.
Keywords
Cite
@article{arxiv.1408.5238,
title = {Approximation properties of simple Lie groups made discrete},
author = {Søren Knudby and Kang Li},
journal= {arXiv preprint arXiv:1408.5238},
year = {2016}
}
Comments
15 pages. Final version. To appear in J. Lie Theory