A characterization of complex hyperbolic Kleinian groups in dimension 3 with trace fields contained in \(\mathbb{R}\)
type: Item
instance of: scholarly article
title: A characterization of complex hyperbolic Kleinian groups in dimension 3 with trace fields contained in \(\mathbb{R}\)
zbMATH Open document ID: 1294.22008
author: Joonhyung Kim
author: Sungwoon Kim
published in: Linear Algebra and its Applications
publication date: 2014-06-18T00:00:00Z
full work available at URL: https://arxiv.org/abs/1401.4244
review text: The authors show that \(\Gamma<\text{SU}(3,1)\) is a non-elementary complex hyperbolic Kleinian group in which \(\text{tr}(\gamma)\in\mathbb{R}\) for all \(\gamma\in \Gamma\) if and only if \(\Gamma\) is conjugate to a subgroup of \(\text{SO}(3,1)\) or \(\text{SU}(1,1)\times \text{SU}(2)\). -- This result is an easy consequence of Satz 1 by [\textit{G. Kern-Isberner} and \textit{G. Rosenberger}, Result. Math. 6, 40--47 (1983; Zbl 0517.20023)].
Mathematics Subject Classification ID: 22E40
Mathematics Subject Classification ID: 30F40
Mathematics Subject Classification ID: 57S30
zbMATH DE Number: 6305122
zbMATH Keywords: Kleinian groups
zbMATH Keywords: Fuchsian groups
zbMATH Keywords: trace fields
reviewed by: Gerhard Rosenberger
MaRDI profile type: Publication
OpenAlex ID: W2035342980
arXiv ID: 1401.4244
cites work: A characterization of Fuchsian groups acting on complex hyperbolic spaces
cites work: Q4237093
cites work: Reversible complex hyperbolic isometries
cites work: Quaternionic hyperbolic Fuchsian groups.
cites work: Q4039828
DOI: 10.1016/J.LAA.2014.05.003
Recommended article: Complex and quaternionic hyperbolic Kleinian groups with real trace fields
Recommended article: A note on trace fields of complex hyperbolic groups
Recommended article: A note on complex-hyperbolic Kleinian groups
Recommended article: A characterization of quaternionic Kleinian groups in dimension 2 with complex trace fields
Recommended article: THE TRACE FUNCTION AND COMPLEX KLEINIAN GROUPS IN $P_{\mathbb{C}}^{2}$
Recommended article: A Survey of Complex Hyperbolic Kleinian Groups
Recommended article: A note on Trace-Fields of Kleinian Groups
Recommended article: Q4884382
Recommended article: Q3135236
Recommended article: Traces in complex hyperbolic triangle groups
description: scientific article