b-Structures on Lie groups and Poisson reduction
We introduce the notion of b-Lie group as a pair(G, H) where Gis a Lie group and H is a codimension-one Lie subgroup, and study the associated canonical b-symplectic structure on the b-cotangent bundle bT*G together with its reduction theory. Namely, we prove that the Poisson reduction under the cot...
| Autores: | , , |
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| Tipo de recurso: | informe técnico |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/336020 |
| Acceso en línea: | https://hdl.handle.net/2117/336020 |
| Access Level: | acceso abierto |
| Palabra clave: | Classificació AMS::22 Topological groups, lie groups Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | We introduce the notion of b-Lie group as a pair(G, H) where Gis a Lie group and H is a codimension-one Lie subgroup, and study the associated canonical b-symplectic structure on the b-cotangent bundle bT*G together with its reduction theory. Namely, we prove that the Poisson reduction under the cotangent lifted action of H by left translations is globally isomorphic to a product of the minus Lie Poisson structure on h* (where h is the Lie algebra of H) and the canonical b-symplectic structure on bT*(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. |
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