TEST MAP AND DISCRETENESS IN SL(2, ℍ)

Abstract

Let H, be the division ring of real quaternions. Let SL(2, H) be the group of 2 × 2 quaternionic matrices with quaternionic determinant det A = |ad -aca-1b| = 1. This group acts by the orientation-preserving isometries of the five-dimensional real hyperbolic space. We obtain discreteness criteria for Zariski-dense subgroups of SL(2, H).