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Derived brackets

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arxiv math/0312524 v1 pith:FSTLO5NI submitted 2003-12-31 math.DG math.SG

Yvette Kosmann-Schwarzbach This is my paper · ORCID
classification math.DGmath.SG
keywords bracketsderivedbracketpoissonrespalgebrasalgebroidbundle
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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".

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Supersymmetry and the Suzuki chain

    math.QA 2019-08 accept novelty 8.0 of 10

    All such SVOAs are exactly two infinite families plus nine exceptional examples, with automorphism groups ranging from symmetric groups to the Suzuki chain and related centralizers.

  2. Generalised Complex and Spinor Relations

    hep-th 2026-03 unverdicted novelty 7.0 of 10

    Courant algebroid relations define spinor and Dirac structure relations, with T-duality inducing spinor relations that generalize twisted cohomology isomorphisms and are compatible with Type II supergravity equations.

  3. Nambu variant of Local Resolution of Problem of Time and Background Independence

    gr-qc 2019-08 reject novelty 5.0 of 10

    The paper extends a local resolution of the Problem of Time to Nambu n-ary bracket formalism, introducing Nambu-Dirac and Nambu algorithms and a claimed uniqueness theorem for Nambu observables.

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