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.
Categories: math.GR math.AG