Abstract
LetF\mathbb {F}denote either the complex numbersC\mathbb {C}or the quaternionsH\mathbb {H}. LetHFn\mathbf {H}_{\mathbb {F}}^ndenote thenn-dimensional hyperbolic space overF\mathbb {F}. We obtain algebraic criteria to classify the isometries ofHFn\mathbf {H}_{\mathbb {F}}^n. This generalizes the work in Geom. Dedicata157(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 ofHCn\mathbf {H}_{\mathbb {C}}^nis also obtained.
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