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ISRN Geometry
Volume 2012 (2012), Article ID 757489, 12 pages
doi:10.5402/2012/757489
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 quaternionic matrices to obtain this characterization. Another characterization in terms of conjugacy invariants is also given.