De Sole, A., Kac, V. G. and Valeri, D. (2015) Double Poisson vertex algebras and non-commutative Hamiltonian equations. Advances in Mathematics, 281, pp. 1025-1099. (doi: 10.1016/j.aim.2015.05.011)
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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.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Valeri, Dr Daniele |
| Authors: | De Sole, A., Kac, V. G., and Valeri, D. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Advances in Mathematics |
| Publisher: | Elsevier |
| ISSN: | 0001-8708 |
| ISSN (Online): | 1090-2082 |
| Published Online: | 17 June 2015 |
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