## Hiroshima Mathematical Journal

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

### Extremality of quaternionic Jørgensen inequality

Krishnendu Gongopadhyay and Abhishek Mukherjee

#### 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

**Digital Object Identifier**

doi:10.32917/hmj/1499392822

**Mathematical Reviews number (MathSciNet)**

MR3679886

**Zentralblatt MATH identifier**

06775344

**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. doi:10.32917/hmj/1499392822. https://projecteuclid.org/euclid.hmj/1499392822