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

- Haisheng Li,
*Vertex algebras and vertex Poisson algebras*, Commun. Contemp. Math. http://arxiv.org/abs/math/0209310 - A. De Sole, V. G. Kac, M.; Wakimoto,
*On classification of Poisson vertex algebras*, Transform. Groups**15**(2010), no. 4, 883–907 MR2012a:17051 doi - B. Bakalov, A. De Sole,
*Non-linear Lie conformal algebras with three generators*, Selecta Math. (N.S.) 14 (2009), no. 2, 163–198 dpo MR2009m:17024 - 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 - Gaywalee Yamskulna,
*Vertex Poisson algebras associated with Courant algebroids and their deformations; I*, math.QA/0509122 - A. De Sole,
*Poisson vertex algebras in the theory of Hamiltonian equations*, Talk at Algebraic Lie Theory, Newton Inst. U. Cambridge 2009, video

Non-local Poisson vertex algebras are studied with applications to the study of integrability of Hamiltonian PDE-s in

- Alberto De Sole, Victor G. Kac,
*Non-local Hamiltonian structures and applications to the theory of integrable systems I*, arxiv/1210.1688;*II*, arxiv/1211.2391; merged version, arxiv/1302.0148 - Aliaa Barakat, Alberto De Sole, Victor G. Kac,
*Poisson vertex algebras in the theory of Hamiltonian equations*, arxiv/0907.1275

Last revised on February 6, 2013 at 17:20:08. See the history of this page for a list of all contributions to it.