Uniform Kazhdan constant for some families of linear groups

[摘要] Let R be a ring generated by 1 elements with stable range r. Assume that the group ELd (R) has Kazhdan constant epsilon(0) > 0 for some d >= r + 1. We prove that there exist epsilon(epsilon(0), 1) > 0 and k is an element of N, s.t. for every n >= d, ELn(R) has a generating set of order k and a Kazhdan constant larger than E. As a consequence, we obtain for SLn(Z) where n >= 3, a Kazhdan constant which is independent of n w.r.t. generating set of a fixed size. (c) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-12-15

[关键词] unitary representation;Kazhdan property (T);elementary linear group