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• W3037272756 abstract "We survey the many instances of derived bracket construction in differential geometry, Lie algebroid and Courant algebroid theories, and their properties. We recall and compare the constructions of Buttin and Vinogradov, and we prove that the Vinogradov bracket is the skew-symmetrization of a derived bracket. Odd (resp., even) Poisson brackets on supermanifolds are derived brackets of canonical even (resp., odd) Poisson brackets on their cotangent bundle (resp., parity-reversed cotangent bundle). Lie algebras have analogous properties, and the theory of Lie algebroids unifies the results valid for manifolds on the one hand, and for Lie algebras on the other. We outline the role of derived brackets in the theory of Poisson structures with background." @default.
• W3037272756 created "2020-07-02" @default.
• W3037272756 creator A5024875537 @default.
• W3037272756 date "2004-07-01" @default.
• W3037272756 modified "2023-09-25" @default.
• W3037272756 title "Derived Brackets" @default.
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• W3037272756 doi "https://doi.org/10.1007/s11005-004-0608-8" @default.
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