A Note on Quaternionic Hyperbolic Ideal Triangle Groups

Cao, Wensheng ; Huang, Xiaolin

Canadian mathematical bulletin, Tome 59 (2016) no. 2, pp. 244-257

Résumé

In this paper, the quaternionic hyperbolic ideal triangle groups are parametrized by a real one-parameter family $\{{{\phi }_{s}}\,:\,s\,\in \,\mathbb{R}\}$ . The indexing parameter s is the tangent of the quaternionic angular invariant of a triple of points in $\partial \mathbf{H}_{\mathbb{H}}^{2}$ forming this ideal triangle. We show that if $s>\sqrt{125/3},$ then ${{\phi }_{S}}$ is not a discrete embedding, and if $s\,\le \,\sqrt{3\text{5}}$ , then ${{\phi }_{S}}$ is a discrete embedding.

Détail

DOI : 10.4153/CMB-2015-084-2

Mots-clés : 20F67, 22E40, 30F40, quaternionic inversion, ideal triangle group, quaternionic Cartan angular invariant

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