Double Poisson vertex algebras and non-commutative Hamiltonian equations

Magri F., A simple model of the integrable Hamiltonian equation , J. Math. Phys. 19

1978

Earlier work this paper cites.

Faddeev L.D., Takhtajan L.A., Hamiltonian approach in soliton theory , Nauka, 1986

1986

Earlier work this paper cites.

Dorfman I.Y., Fokas A.S., Hamiltonian theory over non-commutative rings and integrability in multidimensions , J. Math. Phys. 33

1992

Earlier work this paper cites.

Olver P.J., Applications of Lie groups to differential equations , Second edition, Graduate Texts in Mathematics, 107

1993

Earlier work this paper cites.

Kac V.G., Vertex algebras for beginners , University Lecture Series 10 (1998). Second edition. American Mathematical Society, Providence, RI

1998

Earlier work this paper cites.

Olver P.J., Sokolov V.V., Integrable evolution equations on associative algebras , Comm. Math. Phys. 193

1998

Cited alongside, same era.

Kupershmidt B.A., KP or mKP. Noncommutative mathematics of Lagrangian, Hamiltonian, and integrable systems , Mathematical Surveys and Monographs 78

2000

Cited alongside, same era.

Mikhailov A.V., Sokolov V.V., Integrable ODEs on associative algebras , Comm. Math. Phys. 211

2000

Cited alongside, same era.

Crawley-Boevey W., Etingof P., Ginzburg V., Non-commutative geometry and quiver algebras , Adv. Math. 209

2007

Cited alongside, same era.

Van den Bergh M., Double Poisson algebras , Trans. Amer. Math. Soc. 360

Original

2008

Cited alongside, same era.

Barakat A., De Sole A., Kac V.G., Poisson vertex algebras in the theory of Hamiltonian equations , Jpn. J. Math. 4

2009

Later among the works it cites.

De Sole A., Kac V.G., Non-local Poisson structures and applications to the theory of integrable systems , Jpn. J. Math. 8

2013

Later among the works it cites.

Odesskii A., Rubtsov V., Sokolov V., Double Poisson brackets on free associative algebras , in Noncommutative birational geometry, representations and combinatorics, Contemp. Math. 592

2013

Later among the works it cites.

De Sole A., Kac V.G., Valeri D., Dirac reduction for Poisson vertex algebras , Comm. Math. Phys. 331

2014

Closest in time.

De Sole A., Kac V.G., Valeri D., Adler-Gelfand-Dickey approach to classical 𝒲 \mathcal{W} -algebras within the theory of Poisson vertex algebras , IMRN 2015; doi: 10.1093/imrn/rnv017

2015