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On double Poisson structures on commutative algebras

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arxiv 1603.07553 v2 pith:KE4IY3ZL submitted 2016-03-24 math.QA

Geoffrey Powell This is my paper · ORCID
classification math.QA
keywords structuresdoublepoissonalgebrascommutativealgebraberghpolynomial
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Double Poisson structures (a la Van den Bergh) on commutative algebras are studied; the main result shows that there are no non-trivial such structures on polynomial algebras of Krull dimension greater than one. For a general commutative algebra A, this places significant restrictions on possible double Poisson structures. Exotic double Poisson structures are exhibited by the case of the polynomial algebra on a single generator, previously considered by Van den Bergh.

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Cited by 2 Pith papers

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

  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.

  2. Coupled double Poisson brackets

    math.QA 2026-05 unverdicted novelty 7.0 of 10

    Introduces coupled double Poisson brackets, proves bijection to wheeled Poisson brackets, and gives correspondences to Poisson-left-pre-Lie algebras and Yang-Baxter solutions on free polynomial algebras.

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