Nonlinearity of matrix groups

2009/04/21 by Martin Kassabov, Kassabov, Martin, Mark Sapir +1
Mathematics · #20G15 #20H20 #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras #math.GR #msc:20G15 #msc:20H20

paper · pdf · doi:10.48550/arxiv.0904.3153

8 pages, no figures; v3: a question about EL_2 from the first version is answered

openalex publication_date 2009/04/21 · arxiv created 2009/05/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this note is to answer a question by Guoliang Yu of whether the group EL₃(Z<x,y>), where Z<x,y> is the free (non-commutative) ring, has any faithful linear representations over a field. We prove, in particular, that for every (unitary associative) ring R, the group EL₃(R) has a faithful finite dimensional complex representation if and only if R has a finite index ideal that has a faithful finite dimensional complex representation.

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