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Article contents
Reversibility of affine transformations
Part of:
Classical differential geometry
Structure and classification of infinite or finite groups
Complex spaces with a group of automorphisms
Special matrices
Automorphic functions
Published online by Cambridge University Press: 08 November 2023
Abstract
An element g in a group G is called reversible if g is conjugate to g−1 in G. An element g in G is strongly reversible if g is conjugate to g−1 by an involution in G. The group of affine transformations of 
$\mathbb D^n$ may be identified with the semi-direct product 
$\mathrm{GL}(n, \mathbb D) \ltimes \mathbb D^n $, where 
$\mathbb D:=\mathbb R, \mathbb C$ or 
$ \mathbb H $. This paper classifies reversible and strongly reversible elements in the affine group 
$\mathrm{GL}(n, \mathbb D) \ltimes \mathbb D^n $.
Keywords
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 66 , Issue 4 , November 2023 , pp. 1217 - 1228
- Copyright
- © The Author(s), 2023. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.
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