Pith. sign in

REVIEW 2 cited by

Double Poisson vertex algebras and non-commutative Hamiltonian equations

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1410.3325 v2 pith:GQAM2OPK submitted 2014-10-13 math-ph math.MPmath.RAmath.RTnlin.SI

Alberto De Sole , Victor G. Kac , Daniele Valeri This is my paper · ORCID
classification math-phmath.MPmath.RAmath.RTnlin.SI
keywords algebrasdoublenon-commutativepoissonvertexhamiltoniantheoryaimed
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

We develop the formalism of double Poisson vertex algebras (local and non-local) aimed at the study of non-commutative Hamiltionan PDEs. This is a generalization of the theory of double Poisson algebras, developed by Van den Bergh, which is used in the study of Hamiltonian ODEs. We apply our theory of double Poisson vertex algebras to non-commutative KP and Gelfand-Dickey hierarchies. We also construct the related non-commutative de Rham and variational complexes.

Discussion (0). Continue with ORCID to comment.

Forward citations

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.

Pith tools