Classification of quaternionic hyperbolic isometries

Gongopadhyay, Krishnendu; Parsad, Shiv

doi:10.1090/S1088-4173-2013-00256-7

Classification of quaternionic hyperbolic isometries
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by Krishnendu Gongopadhyay and Shiv Parsad PDF

Conform. Geom. Dyn. 17 (2013), 68-76 Request permission

Abstract:

Let $\mathbb {F}$ denote either the complex numbers $\mathbb {C}$ or the quaternions $\mathbb {H}$. Let $\mathbf {H}_{\mathbb {F}}^n$ denote the $n$-dimensional hyperbolic space over $\mathbb {F}$. We obtain algebraic criteria to classify the isometries of $\mathbf {H}_{\mathbb {F}}^n$. This generalizes the work in Geom. Dedicata 157 (2012), 23–39 and Proc. Amer. Math. Soc. 141 (2013), 1017–1027, to isometries of arbitrary dimensional quaternionic hyperbolic space. As a corollary, a characterization of isometries of $\mathbf {H}_{\mathbb {C}}^n$ is also obtained.

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