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Zbl 1190.37022
Gongopadhyay, Krishnendu
Algebraic characterization of the isometries of the hyperbolic 5-space. (English)
[J] Geom. Dedicata 144, 157-170 (2010). ISSN 0046-5755; ISSN 1572-9168/e

The author obtains an algebraic characterization of the dynamical types of the orientation preserving isometries of the hyperbolic 5-space $\Bbb{H}^5$. The characterization is described by using the representation of the isometries of $\Bbb{H}^5$ as $2 \times 2$ matrices over the quaternions, $\bbfG\bbfL(2,\mathbb{H})$, together with the natural embedding of $\bbfG\bbfL(2,\mathbb{H})$ into $\bbfG\bbfL(4,\mathbb{C})$. It is also given the determination of the conjugacy classes and the $z$-classes in $\bbfG\bbfL(2,\mathbb{H})$.
[Kazuhiro Ichihara (Tokyo)]

MSC 2000:: *37C85 Dynamics of group actions other than $\bbfZ$ and $\bbfR$, etc.
51M10 Hyperbolic and elliptic geometries (general) and generalizations
15A33 Matrices over special rings

Keywords: hyperbolic 5-space; isometries; quaternions; $z$-classes

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Zentralblatt MATH Berlin [Germany]