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Reversible maps in the group of quaternionic Möbius transformations

Published online by Cambridge University Press:  01 July 2007

ROMAN LÁVIČKA ,
ANTHONY G. O'FARRELL  and
IAN SHORT
ROMAN LÁVIČKA
Affiliation:
Mathematical Institute, Charles University, Prague, Czech Republic. e-mail: lavicka@karlin.mff.cuni.cz
ANTHONY G. O'FARRELL
Affiliation:
National University of Ireland, Maynooth, Ireland. e-mail: anthonyg.ofarrell@gmail.com
IAN SHORT
Affiliation:
National University of Ireland, Maynooth, Ireland. e-mail: ian.short@nuim.ie
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Abstract

The reversible elements of a group are those elements that are conjugate to their own inverse. A reversible element is said to be reversible by an involution if it is conjugate to its own inverse by an involution. In this paper, we classify the reversible elements and the elements reversible by involutions in the group of quaternionic Möbius transformations.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 1 , July 2007 , pp. 57 - 69
Copyright
Copyright © Cambridge Philosophical Society 2007

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