Hiroshima Mathematical Journal

Extremality of quaternionic Jørgensen inequality

Krishnendu Gongopadhyay and Abhishek Mukherjee

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

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1499392822

Subjects
Primary: 20H10: Fuchsian groups and their generalizations [See also 11F06, 22E40, 30F35, 32Nxx]
Secondary: 51M10: Hyperbolic and elliptic geometries (general) and generalizations 20H25: Other matrix groups over rings

Keywords
quaternionic matrices Jørgensen inequality hyperbolic 5-space

Citation

Gongopadhyay, Krishnendu; Mukherjee, Abhishek. Extremality of quaternionic Jørgensen inequality. Hiroshima Math. J. 47 (2017), no. 2, 113--137. https://projecteuclid.org/euclid.hmj/1499392822.


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