On abstract representations of the groups of rational points of algebraic groups and their deformations

Details On abstract representations of the groups of rational points of algebraic groups and their deformations On abstract representations of the groups of rational points of algebraic groups and their deformations

2011-11-27

arxiv.org/abs/1111.6292v2

Mathematics

Group Theory

minor corrections, typos fixed

Scientific paper

In this paper, we continue our study of abstract representations of elementary subgroups of Chevalley groups of rank $\geq 2.$ First, we extend our earlier methods to analyze representations of elementary groups over arbitrary associative rings, and as a consequence, prove the conjecture of Borel and Tits on abstract homomorphisms of the groups of rational points of algebraic groups for groups of the form ${\bf SL}_{n,D}$, where $D$ is a finite-dimensional central division algebra over a field of characteristic zero. Second, we apply our results to study deformations of representations of elementary subgroups of universal Chevalley groups of rank $\geq 2$ over finitely generated commutative rings.

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