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A presentation for the Eisenstein-Picard modular group in three complex dimensions

Part of: Lie groups Other groups of matrices Real and complex geometry Special aspects of infinite or finite groups

Published online by Cambridge University Press:  25 July 2023

Jieyan Wang  and
Baohua Xie Open the ORCID record for Baohua Xie [Opens in a new window]
Jieyan Wang
Affiliation:
School of Mathematics, Hunan University, Changsha 410082, P.R. China
Baohua Xie*
Affiliation:
School of Mathematics, Hunan University, Changsha 410082, P.R. China
*
Corresponding author: Baohua Xie; Email: xiexbh@hnu.edu.cn
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Abstract

A. Mark and J. Paupert [Presentations for cusped arithmetic hyperbolic lattices, 2018, arXiv:1709.06691.] presented a method to compute a presentation for any cusped complex hyperbolic lattice. In this note, we will use their method to give a presentation for the Eisenstein-Picard modular group in three complex dimensions.

Keywords

Complex hyperbolic spaceEisenstein-Picard modular groupCoarse fundamental domain

MSC classification

Primary: 22E40: Discrete subgroups of Lie groups
Secondary: 20F05: Generators, relations, and presentations 20H10: Fuchsian groups and their generalizations 51M10: Hyperbolic and elliptic geometries (general) and generalizations
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 65 , Issue 3 , September 2023 , pp. 625 - 654
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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