A presentation of the group Sl * (2, A), A a simple artinian ring with involution

Abstract

Let (A,*) be an involutive ring. Then the groups Sl*(2, A), are a non commutative version of the special linear groups Sl(2, F) defined over a field F. In particular, if A = M(n, F) and * is transposition, then Sl*(2, Mn(F)) = Sp(2n, F). The above groups were defined by Pantoja and Soto-Andrade, and a set of generators for the group SSl*(2, A) (which is either Sl*(2, A) or a index 2 subgroup of Sl*(2, A)) was given in the case when A is an artinian ring. In this paper, we prove that the mentioned generators provide a presentation of the mentioned groups in the case of simple artinian rings.