Lifts of Poisson structures to Weil bundles
نویسنده
چکیده
In the present paper, we study complete and vertical lifts of tensor fields from a smooth manifoldM to its Weil bundle TM defined by a Frobenius Weil algebra A. For a Poisson manifold (M,w), we show that the complete lift w and the vertical lift w of the Poisson tensor w are Poisson tensors on TM and establish their properties. We prove that the complete and the vertical lifts induce homomorphisms of the Poisson cohomology spaces. We compute the modular classes of the lifts of Poisson structures. 2000 MSC: 53D17, 58A32.
منابع مشابه
On characterization of Poisson and Jacobi structures
We characterize Poisson and Jacobi structures by means of complete lifts of the corresponding tensors: the lifts have to be related to canonical structures by morphisms of corresponding vector bundles. Similar results hold for generalized Poisson and Jacobi structures (canonical structures) associated with Lie algebroids and Jacobi algebroids. MSC 2000: 17B62 17B66 53D10 53D17
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تاریخ انتشار 2009