Nonlinearity of matrix groups

Details Nonlinearity of matrix groups Nonlinearity of matrix groups

2009-04-21

arxiv.org/abs/0904.3153v3

Mathematics

Group Theory

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

Scientific paper

The aim of this note is to answer a question by Guoliang Yu of whether the group $EL_3(Z)$, where $Z$ 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.

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