Uniform Kazhdan Constant for some families of linear groups

2006/12/14 by Uzy Hadad, Hadad, Uzy
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT

paper · pdf · doi:10.48550/arxiv.math/0612390

To appear in J. of Alg

openalex publication_date 2006/12/14 · arxiv created 2007/09/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be a ring generated by l elements with stable range r. Assume that the group EL_d(R) has Kazhdan constant ε₀>0 for some d > r . We prove that there exist ε(ε₀,l) >0 and k ∈ N, s.t. for every n ≥ d, EL_n(R) has a generating set of order k and a Kazhdan constant larger than ε. As a consequence, we obtain for SL_n(Z) where n ≥ 3, a Kazhdan constant which is independent of n w.r.t generating set of a fixed size.

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