b-Structures on Lie groups and Poisson reduction
Motivated by the group of Galilean transformations and the subgroup of Galilean transformations which fix time zero, we introduce the notion of a b-Lie group as a pair (G,H) where G is a Lie group and H is a codimension-one Lie subgroup. Such a notion allows us to give a theoretical framework for tr...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/531807 |
| Acceso en línea: | http://hdl.handle.net/2072/531807 |
| Access Level: | acceso abierto |
| Palabra clave: | b-Symplectic manifolds Cotangent models Galilean transformations Lie groups Minimal coupling Poisson reduction |
| Sumario: | Motivated by the group of Galilean transformations and the subgroup of Galilean transformations which fix time zero, we introduce the notion of a b-Lie group as a pair (G,H) where G is a Lie group and H is a codimension-one Lie subgroup. Such a notion allows us to give a theoretical framework for transformations of space-time where the initial time can be seen as a boundary. In this theoretical framework, we develop the basics of the theory and study the associated canonical b-symplectic structure on the b-cotangent bundle T⁎bG together with its reduction theory. Namely, we extend the minimal coupling procedure to T⁎bG/H and prove that the Poisson reduction under the cotangent lifted action of H by left translations can be described in terms of the Lie Poisson structure on h⁎ (where h is the Lie algebra of H) and the canonical b-symplectic structure on T⁎b(G/H), where G/H is viewed as a one-dimensional b-manifold having as critical hypersurface (in the sense of b-manifolds) the identity element. © 2022 The Author(s) |
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