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# Free Groups Generated by Two Heisenberg Translations

Published:2012-12-29
Printed: Dec 2013
• BaoHua Xie,
College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China
• JieYan Wang,
College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China
• YuePing Jiang,
College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China
 Format: LaTeX MathJax PDF

## Abstract

In this paper, we will discuss the groups generated by two Heisenberg translations of $\mathbf{PU}(2,1)$ and determine when they are free.
 Keywords: free group, Heisenberg group, complex triangle group
 MSC Classifications: 30F40 - Kleinian groups [See also 20H10] 22E40 - Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx] 20H10 - Fuchsian groups and their generalizations [See also 11F06, 22E40, 30F35, 32Nxx]

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