Jacobi Structures on Affine Bundles
| Autor: | Janusz Grabowski, Juan Carlos Marrero, Pawel Urbanski, D. Iglesias, Edith Padrón |
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| Rok vydání: | 2006 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics Applied Mathematics General Mathematics 81S10 Type (model theory) Affine plane Algebra Affine geometry 53D17 53D05 Differential Geometry (math.DG) Affine geometry of curves Affine representation Mathematics - Symplectic Geometry Poisson manifold Affine group FOS: Mathematics Symplectic Geometry (math.SG) Affine bundle Mathematics::Symplectic Geometry Mathematics |
| Zdroj: | Acta Mathematica Sinica, English Series. 23:769-788 |
| ISSN: | 1439-7617 1439-8516 |
| DOI: | 10.1007/s10114-005-0716-0 |
| Popis: | We study affine Jacobi structures on an affine bundle $\pi:A\to M$, i.e. Jacobi brackets that close on affine functions. We prove that there is a one-to-one correspondence between affine Jacobi structures on $A$ and Lie algebroid structures on the vector bundle $A^+=\bigcup_{p\in M}Aff(A_p,\R)$ of affine functionals. Some examples and applications, also for the linear case, are discussed. For a special type of affine Jacobi structures which are canonically exhibited (strongly-affine or affine-homogeneous Jacobi structures) over a real vector space of finite dimension, we describe the leaves of its characteristic foliation as the orbits of an affine representation. These affine Jacobi structures can be viewed as an analog of the Kostant-Arnold-Liouville linear Poisson structure on the dual space of a real finite-dimensional Lie algebra. Comment: 26 pages; minor changes, one reference added. The final version to appear in Acta Math. Sinica, English Series |
| Databáze: | OpenAIRE |
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