%0 Journal Article
%T Nonlinearity of matrix groups
%A Martin Kassabov
%A Mark Sapir
%J Mathematics
%D 2009
%I arXiv
%X The aim of this note is to answer a question by Guoliang Yu of whether the group $EL_3(Z<x,y>)$, 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 $EL_3(R)$ 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.
%U http://arxiv.org/abs/0904.3153v3