Geometry of infinite dimensional Cartan Developments

The Cartan development takes a Lie algebra valued 1-form satisfying the Maurer-Cartan equation on a simply connected manifold \(M\) to a smooth mapping from \(M\) into the Lie group. In this paper this is generalized to infinite dimensional \(M\) for infinite dimensional regular Lie groups. The Cart...

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Bibliographic Details
Published in:arXiv.org 2024-08
Main Authors: Michor, Johanna, Michor, Peter W
Format: Article
Language:English
Subjects:
Lie groups
Mapping
Online Access:Get full text
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Summary:The Cartan development takes a Lie algebra valued 1-form satisfying the Maurer-Cartan equation on a simply connected manifold \(M\) to a smooth mapping from \(M\) into the Lie group. In this paper this is generalized to infinite dimensional \(M\) for infinite dimensional regular Lie groups. The Cartan development is viewed as a generalization of the evolution map of a regular Lie group. The tangent mapping of a Cartan development is identified as another Cartan development.
ISSN:2331-8422