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ISRN Geometry
Volume 2012 (2012), Article ID 757489, 12 pages
http://dx.doi.org/10.5402/2012/757489
Research Article

Algebraic Characterization of Isometries of the Hyperbolic 4-Space

Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, SAS Nagar, Sector 81, P.O. Mohali 140306, India

Received 20 November 2011; Accepted 8 December 2011

Academic Editor: S. Hernández

Copyright © 2012 Krishnendu Gongopadhyay. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We classify isometries of the real hyperbolic 4-space by their conjugacy classes of centralizers. We use the representation of the isometries by 2 × 2 quaternionic matrices to obtain this characterization. Another characterization in terms of conjugacy invariants is also given.