Jørgensen’s Inequality and Algebraic Convergence Theorem in Quaternionic Hyperbolic Isometry Groups

Abstract EN

We obtain an analogue of Jørgensen's inequality in quaternionic hyperbolic space.

As an application, we prove that if the r-generator quaternionic Kleinian group satisfies I-condition, then its algebraic limit is also a quaternionic Kleinian group.

Our results are generalizations of the counterparts in the n-dimensional real hyperbolic space.