A Note on Quaternionic Hyperbolic Ideal Triangle Groups
Canadian mathematical bulletin, Tome 59 (2016) no. 2, pp. 244-257
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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.
Mots-clés :
20F67, 22E40, 30F40, quaternionic inversion, ideal triangle group, quaternionic Cartan angular invariant
Cao, Wensheng; Huang, Xiaolin. A Note on Quaternionic Hyperbolic Ideal Triangle Groups. Canadian mathematical bulletin, Tome 59 (2016) no. 2, pp. 244-257. doi: 10.4153/CMB-2015-084-2
@article{10_4153_CMB_2015_084_2,
author = {Cao, Wensheng and Huang, Xiaolin},
title = {A {Note} on {Quaternionic} {Hyperbolic} {Ideal} {Triangle} {Groups}},
journal = {Canadian mathematical bulletin},
pages = {244--257},
year = {2016},
volume = {59},
number = {2},
doi = {10.4153/CMB-2015-084-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-084-2/}
}
TY - JOUR AU - Cao, Wensheng AU - Huang, Xiaolin TI - A Note on Quaternionic Hyperbolic Ideal Triangle Groups JO - Canadian mathematical bulletin PY - 2016 SP - 244 EP - 257 VL - 59 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-084-2/ DO - 10.4153/CMB-2015-084-2 ID - 10_4153_CMB_2015_084_2 ER -
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