Algebraic characterization of the isometries of the hyperbolic 5-space

2008/08/31 by Krishnendu Gongopadhyay
Mathematics · #math.GT #math.DS #msc:51M10 #msc:37C85

paper · pdf

published as Geom. Dedicata 144 (2010), no.1, 157--170. · revised and reorganized version

Abstract

Using the representation of the isometries as 2x2 invertible matrices over the division algebra \H of quaternions, we give an algebraic characterization of the dynamical types of the orientation-preserving isometries of the hyperbolic 5-space. We also determine the conjugacy classes and the conjugacy classes of centralizers or the z-classes in GL(2, \H).

Cited by

• Dynamical Types of Isometries of the Hyperbolic Space