nLab Poisson vertex algebra




A Poisson vertex algebra is a unital commutative associative algebra with a derivation and a λ\lambda-bracket; it has to satisfy the axioms of a Lie conformal algebra; and the λ\lambda-bracket and the multiplication form a Poisson algebra (i.e. satisfy the Leibniz rule). It is a Poisson analogue of a conformal Lie algebra.

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  • Alberto De Sole, Victor G. Kac, Daniele Valeri, Classical W-algebras and Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras, arxiv/1207.6286
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On non-local Poisson vertex algebras with applications to the study of integrability of Hamiltonian PDEs in

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