Adler-Oevel-Ragnisco type operators and Poisson vertex algebras

2022/07/30 by Alberto De Sole, De Sole, Alberto, Victor G. Kač +3
Mathematics · Physics and Astronomy · #17B69 #37K10 #37K30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2208.00154

openalex publication_date 2022/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The theory of triples of Poisson brackets and related integrable systems, based on a classical R-matrix R in End_F(g), where g is a finite dimensional associative algebra over a field F viewed as a Lie algebra, was developed by Oevel-Ragnisco and Li-Parmentier [OR89,LP89]. In the present paper we develop an "affine" analogue of this theory by introducing the notion of a continuous Poisson vertex algebra and constructing triples of Poisson lambda-brackets. We introduce the corresponding Adler type identities and apply them to integrability of hierarchies of Hamiltonian PDEs.

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