Double Poisson vertex algebras and non-commutative Hamiltonian equations

Author(s)
De Sole, Alberto; Valeri, Daniele; Kac, Victor
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Abstract
We develop the formalism of double Poisson vertex algebras (local and non-local) aimed at the study of non-commutative Hamiltonian PDEs. This is a generalization of the theory of double Poisson algebras, developed by Van den Bergh, which is used in the study of Hamiltonian ODEs. We apply our theory of double Poisson vertex algebras to non-commutative KP and Gelfand-Dickey hierarchies. We also construct the related non-commutative de Rham and variational complexes. Keywords: Double derivations; Double Poisson algebra; Double Poisson vertex algebra; Integrable non-commutative Hamiltonian equation; Non-commutative de Rham and variational complexes; Non-commutative KP and Gelfand–Dickey equations
Date issued
2015-06
URI
http://hdl.handle.net/1721.1/115829
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Advances in Mathematics
Publisher
Elsevier
Citation
De Sole, Alberto et al. “Double Poisson Vertex Algebras and Non-Commutative Hamiltonian Equations.” Advances in Mathematics 281 (August 2015): 1025–1099 © 2015 Elsevier Inc
Version: Author's final manuscript
ISSN
0001-8708
1090-2082
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