Algebraic characterization of isometries of the complex and the quaternionic hyperbolic planes
| dc.contributor.author | Gongopadhyay, Krishnendu | |
| dc.date.accessioned | 2013-05-02T07:28:44Z | |
| dc.date.available | 2013-05-02T07:28:44Z | |
| dc.date.issued | 2012 | |
| dc.description | Only IISERM authors are available in the record. | |
| dc.description.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. | en_US |
| dc.identifier.citation | Geometriae Dedicata, 157 (1), pp. 23-39 | en_US |
| dc.identifier.uri | http://link.springer.com/article/10.1007%2Fs10711-011-9599-7?LI=true | en_US |
| dc.identifier.uri | 10.1007/s10711-011-9599-7 | en_US |
| dc.language.iso | en | en_US |
| dc.publisher | Springer Science+Business Media B.V. | en_US |
| dc.subject | Classification of isometries | en_US |
| dc.subject | Complex and quaternionic hyperbolic space | en_US |
| dc.subject | z-class | en_US |
| dc.title | Algebraic characterization of isometries of the complex and the quaternionic hyperbolic planes | en_US |
| dc.type | Article | en_US |