Nonlinearity of matrix groups

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dc.creatorKassabov, Martin
dc.creatorSapir, Mark
dc.date2009-04-21
dc.date2009-05-10
dc.date.accessioned2026-07-07T13:12:51Z
dc.date.available2026-07-07T13:12:51Z
dc.descriptionThe 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.
dc.description8 pages, no figures; v3: a question about EL_2 from the first version is answered
dc.identifierhttps://arxiv.org/abs/0904.3153
dc.identifierhttp://arxiv.org/abs/0904.3153
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/229706
dc.subjectGroup Theory
dc.subject20G15, 20H20
dc.titleNonlinearity of matrix groups
dc.typetext

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