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.
Citation
Krishnendu Gongopadhyay. Abhishek Mukherjee. "Extremality of quaternionic Jørgensen inequality." Hiroshima Math. J. 47 (2) 113 - 137, July 2017. https://doi.org/10.32917/hmj/1499392822
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