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Differential calculus over double Lie algebroids

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arxiv 1712.05619 v3 pith:STXVLWPV submitted 2017-12-15 math.RA

Sophie Chemla This is my paper · ORCID
classification math.RA
keywords doublealgebroidscalculusdifferentialalgebroidberghcasecases
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The notion of double Lie algebroid was defined by M. Van den Bergh and was illustrated by the double quasi Poisson case. We give new examples of double Lie algebroids and develop a differential calculus in that context. We recover the non commutative de Rham complex and the double Poisson-Lichnerowicz cohomology (Pichereau-vanWeyer) as particular cases of our construction.

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  1. Double Poisson (vertex) algebra cohomology

    math.RT 2025-09 accept novelty 8.0 of 10

    The authors define a completed double Poisson cohomology valid for all double Poisson brackets, and introduce three cohomology theories for double Poisson vertex algebras, with representation functor compatibility.

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