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http://hdl.handle.net/123456789/141
Title: | Algebraic characterization of isometries of the complex and the quaternionic hyperbolic planes |
Authors: | Gongopadhyay, Krishnendu |
Keywords: | Classification of isometries Complex and quaternionic hyperbolic space z-class |
Issue Date: | 2012 |
Publisher: | Springer Science+Business Media B.V. |
Citation: | Geometriae Dedicata, 157 (1), pp. 23-39 |
Abstract: | Let H F 2 denote the two dimensional hyperbolic space over F, where F is either the complex numbers ℂ or the quaternions ℍ. It is of interest to characterize algebraically the dynamical types of isometries of H F 2. For F = ℂ, such a characterization is known from the work of Giraud-Goldman. In this paper, we offer an algebraic characterization of isometries of H ℍ 2. Our result restricts to the case F = ℂ and provides another characterization of the isometries of H ℂ 2, which is different from the characterization due to Giraud-Goldman. Two elements in a group G are said to be in the same z-class if their centralizers are conjugate in G. The z-classes provide a finite partition of the isometry group. In this paper, we describe the centralizers of isometries of H F 2 and determine the z-classes. |
Description: | Only IISERM authors are available in the record. |
URI: | http://link.springer.com/article/10.1007%2Fs10711-011-9599-7?LI=true 10.1007/s10711-011-9599-7 |
Appears in Collections: | Research Articles |
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