## Hiroshima Mathematical Journal

### Extremality of quaternionic Jørgensen inequality

#### Abstract

Let $\mathrm{SL}(2,\mathbb{H})$ be the group of $2 × 2$ quaternionic matrices with Dieudonné determinant one. The group $\mathrm{SL}(2,\mathbb{H})$ acts on the five dimensional hyperbolic space by isometries. We investigate extremality of Jørgensen type inequalities in $\mathrm{SL}(2,\mathbb{H})$. Along the way, we derive Jørgensen type inequalities for quaternionic Möbius transformations which extend earlier inequalities obtained by Waterman and Kellerhals.

#### Article information

Source
Hiroshima Math. J. Volume 47, Number 2 (2017), 113-137.

Dates