Nonlinearity of matrix groups (joint with Mark Sapir)

Abstract: In this talk I will discuss when the subgroup EL_3(R) of 3 x 3 invertible matrices over a (non-commutative) ring R has a faithful linear representation over a field K. I will show that in the case of algebraically closed fields of characteristic 0 the group EL_3(R) is linear if and only if R has an ideal of finite index which has a faithful finite dimensional representation over that field. It is interesting to note that in the case of positive characteristic the similar statement is not true.