On abstract representations of the groups of rational points of algebraic groups and their deformations

2011/11/27 by Igor A. Rapinchuk, Rapinchuk, Igor A. · 2 citations
Mathematics · #20G35 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #math.AG #math.GR #msc:20G35

paper · pdf · doi:10.48550/arxiv.1111.6292

minor corrections, typos fixed

openalex publication_date 2011/11/27 · arxiv created 2011/12/26 · arxiv updated 2011/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we continue our study of abstract representations of elementary subgroups of Chevalley groups of rank ≥ 2. First, we extend our earlier methods to analyze representations of elementary groups over arbitrary associative rings, and as a consequence, prove the conjecture of Borel and Tits on abstract homomorphisms of the groups of rational points of algebraic groups for groups of the form \bf SL_n,D, where D is a finite-dimensional central division algebra over a field of characteristic zero. Second, we apply our results to study deformations of representations of elementary subgroups of universal Chevalley groups of rank ≥ 2 over finitely generated commutative rings.

Citations

• Property (T) for groups graded by root systems

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