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

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.

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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

Information

Received: 5 January 2016; Revised: 3 August 2016; Published: July 2017
First available in Project Euclid: 7 July 2017

zbMATH: 06775344
MathSciNet: MR3679886
Digital Object Identifier: 10.32917/hmj/1499392822

Subjects:
Primary: 20H10
Secondary: 20H25, 51M10

Rights: Copyright © 2017 Hiroshima University, Mathematics Program

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Vol.47 • No. 2 • July 2017
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