Geometric dynamics on the automorphism group of principal bundles: geodesic flows, dual pairs and chromomorphism groups

Gay-Balmaz, F, Tronci, C and Vizman, C (2010) Geometric dynamics on the automorphism group of principal bundles: geodesic flows, dual pairs and chromomorphism groups arXiv.

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Abstract

We formulate Euler-Poincar\'e equations on the Lie group Aut(P) of automorphisms of a principal bundle P. The corresponding flows are referred to as EPAut flows. We mainly focus on geodesic flows associated to Lagrangians of Kaluza-Klein type. In the special case of a trivial bundle P, we identify geodesics on certain infinite-dimensional semidirect-product Lie groups that emerge naturally from the construction. This approach leads naturally to a dual pair structure containing \delta-like momentum map solutions that extend previous results on geodesic flows on the diffeomorphism group (EPDiff). In the second part, we consider incompressible flows on the Lie group of volume-preserving automorphisms of a principal bundle. In this context, the dual pair construction requires the definition of chromomorphism groups, i.e. suitable Lie group extensions generalizing the quantomorphism group.

Item Type:	Article
Divisions :	Faculty of Engineering and Physical Sciences > Mathematics
Authors :	Name Email ORCID Gay-Balmaz, F Tronci, C c.tronci@surrey.ac.uk Vizman, C
Date :	3 June 2010
Related URLs :	Author
Depositing User :	Symplectic Elements
Date Deposited :	17 May 2017 12:21
Last Modified :	10 Jun 2019 13:08
URI:	http://epubs.surrey.ac.uk/id/eprint/834963

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