Lie algebraic characterization of manifolds. (English) Zbl 1138.53313
This paper studies Jacobi structures on affine bundles. It is well known that linear Poisson structures are in one-to-one correspondence with Lie algebroid structures on the dual vector bundle. In this paper, the author proves the bijective correspondence between affine Jacobi structures and Lie algebroid structures. The passage from Poisson structures and Lie algebroids to Jacobi structures and Jacobi algebroids is in fact the passage from derivations to first order differential operators. Examples and applications of this passage are also studied.
Reviewer: Angela Gammella-Mathieu (Metz)
MSC:
| 53D17 | Poisson manifolds; Poisson groupoids and algebroids |
| 17B63 | Poisson algebras |
| 17B66 | Lie algebras of vector fields and related (super) algebras |
Keywords:
Jacobi structures; smooth real analytic, Stein manifold; characterization by Lie algebra of linear differential operators; Lie algebroidsReferences:
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