Nonlinearity of matrix groups
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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