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arXiv · 1503.08802

Extremality of Quaternionic J{\o}rgensen Inequality

Krishnendu Gongopadhyay·Abhishek Mukherjee
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Abstract

Let ${\rm SL(2, \mathbb H)}$ be the group of $2 \times 2$ quaternionic matrices with Dieudonn\'e determinant $1$. The group ${\rm SL(2, \mathbb H)}$ acts on the five dimensional hyperbolic space by isometries. We investigate extremality of J\o{}rgensen type inequalities in ${\rm SL(2, \mathbb H)}$. Along the way, we derive J\o{}rgensen type inequalities for quaternionic M\"obius transformations which extend earlier inequalities obtained by Waterman and Kellerhals.

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Krishnendu Gongopadhyay, Abhishek Mukherjee. 2015-03-30. Extremality of Quaternionic J{\o}rgensen Inequality. https://arxiv.org/abs/1503.08802

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