Pith. sign in

REVIEW 1 cited by

Double Poisson brackets on free associative algebras

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 1208.2935 v1 pith:IRBA4XYE submitted 2012-08-14 nlin.SI math.QA

A. Odesskii , V. Rubtsov , V. Sokolov This is my paper · ORCID
classification nlin.SImath.QA
keywords poissondoublebracketsassociativefreequadraticalgebrascase
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

We discuss double Poisson structures in sense of M. Van den Bergh on free associative algebras focusing on the case of quadratic Poisson brackets. We establish their relations with an associative version of Young-Baxter equations, we study a bi-hamiltonian property of the linear-quadratic pencil of the double Poisson structure and propose a classification of the quadratic double Poisson brackets in the case of the algebra with two free generators. Many new examples of quadratic double Poisson brackets are proposed.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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.

Pith tools