Free Groups Generated by Two Heisenberg Translations
Canadian mathematical bulletin, Tome 56 (2013) no. 4, pp. 881-889

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, we will discuss the groups generated by two Heisenberg translations of $\text{PU}\left( 2,1 \right)$ and determine when they are free.
DOI : 10.4153/CMB-2012-042-0
Mots-clés : 30F40, 22E40, 20H10, free group, Heisenberg group, complex triangle group
Xie, BaoHua; Wang, JieYan; Jiang, YuePing. Free Groups Generated by Two Heisenberg Translations. Canadian mathematical bulletin, Tome 56 (2013) no. 4, pp. 881-889. doi: 10.4153/CMB-2012-042-0
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[1] [1] Brenner, J. L., Quelques groupes libres de matrices. C. R. Acad. Sci. Pari. 241 (1955), 1689–1691. Google Scholar

[2] [2] Chang, B., Jenning, S. A., and Ree, R., On certain pairs of matrices which generate free groups. Canad. J. Math. 10 (1958), 279–284. Google Scholar | DOI

[3] [3] Goldman, W. M., Complex hyperbolic geometry. Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1999. Google Scholar

[4] [4] Goldman, W. M. and Parker, J. R., Complex hyperbolic ideal triangle groups. J. Reine Angew. Math. 425 (1992), 71–86. Google Scholar

[5] [5] Lyndon, R. C. and Ullman, J. L., Groups generated by two parabolic linear fractional transformations. Canad. J. Math. 21 (1969), 1388–1403. Google Scholar | DOI

[6] [6] Massey, W. S., Algebraic topology: an introduction. Graduate Texts in Mathematics, 56, Springer-Verlag, New York-Heidelberg, 1977. Google Scholar

[7] [7] Roger, R. C. and Schupp, P. E., Combinatorial group theory. Classics in Mathematics, Springer-Verlag, Berlin, 2001. Google Scholar

[8] [8] Sanov, L. N., A property of a representation of a free group. (Russian) Doklady Akad. Nauk SSS. 57 (1947), 657–659. Google Scholar

[9] [9] Schwartz, R. E., Ideal triangle groups, dented tori, and numerical analysis. Ann. of Math. 153 (2001), no. 3, 533–598. Google Scholar | DOI

[10] [10] Xie, B. and Jiang, Y.,Groups generated by two elliptic elements in (2; 1). Linear Algebra Appl. 433 (2010), no. 11–12, 2168–2177. Google Scholar | DOI

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