A Bijection Between the Adjoint and Coadjoint Orbits of a Semidirect Product

Arathoon, Philip (2019) A Bijection Between the Adjoint and Coadjoint Orbits of a Semidirect Product. Differential Geometry and its Applications, 62. pp. 267-282. ISSN 0926-2245

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Abstract

We prove that there exists a geometric bijection between the sets of adjoint and coadjoint orbits of a semidirect product, provided a similar bijection holds for particular subgroups. We also show that under certain conditions the homotopy types of any two orbits in bijection with each other are the same. We apply our theory to the examples of the affine group and the Poincar ́e group, and discuss the limitations and extent of this result to other groups.

Item Type: Article
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 22 Topological groups, Lie groups
Depositing User: Mr Philip Arathoon
Date Deposited: 12 Jan 2020 09:35
Last Modified: 12 Jan 2020 09:35
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2740

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