A Note on Quaternionic Hyperbolic Ideal Triangle Groups

Abstract

AbstractIn this paper, the quaternionic hyperbolic ideal triangle groups are parametrized by a real one-parameter family {ϕ: s ∊ ℝ}. The indexing parameter s is the tangent of the quaternionic angular invariant of a triple of points in forming this ideal triangle. We show that if , then ϕs is not a discrete embedding, and if s , then ϕs is a discrete embedding.