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Fondements de la théorie des -produits. Notion de -produit de Vey; tout -produit est équivalent à un -produit de Vey. Sur toute variété symplectique paracompacte telle que , il existe des -produits de Vey. Caractérisation des algèbres de Lie engendrées par antisymétrisation d’un -produit (éventuellement faible); ce sont à une équivalence près, les algèbres de Lie de Vey.On considère les variétés symplectiques sur lesquelles opère, par symplectomorphismes, un groupe de Lie . Si admet...
We study several linear connections (the first canonical, the Chern, the well adapted, the Levi Civita, the Kobayashi-Nomizu, the Yano, the Bismut and those with totally skew-symmetric torsion) which can be defined on the four geometric types of -metric manifolds. We characterize when such a connection is adapted to the structure, and obtain a lot of results about coincidence among connections. We prove that the first canonical and the well adapted connections define a one-parameter family of adapted...
We define the divergence operators on a graded algebra, and we show that, given an odd
Poisson bracket on the algebra, the operator that maps an element to the divergence of
the hamiltonian derivation that it defines is a generator of the bracket. This is the
“odd laplacian”, , of Batalin-Vilkovisky quantization. We then study the
generators of odd Poisson brackets on supermanifolds, where divergences of graded vector
fields can be defined either in terms of berezinian volumes or of graded connections.
Examples...
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