Double Poisson vertex algebras and non-commutative Hamiltonian equations

被引：17

作者：

De Sole, Alberto ^{[2
]}

Kac, Victor G. ^{[3
]}

Valeri, Daniele ^{[1
,4
]}

机构：

[1] Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China

[2] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy

[3] MIT, Dept Math, Cambridge, MA 02139 USA

[4] Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China

来源：

ADVANCES IN MATHEMATICS | 2015年 / 281卷

基金：

美国国家科学基金会;

关键词：

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; ASSOCIATIVE ALGEBRAS;

D O I：

10.1016/j.aim.2015.05.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：1025 / 1099

页数：75

共 15 条

[1] Poisson vertex algebras in the theory of Hamiltonian equations
Barakat, Aliaa
De Sole, Alberto
Kac, Victor G.
[J]. JAPANESE JOURNAL OF MATHEMATICS, 2009, 4 (02): : 141 - 252
[2] Noncommutative geometry and quiver algebras
Crawley-Boevey, William
Etingof, Pavel
Ginzburg, Victor
[J]. ADVANCES IN MATHEMATICS, 2007, 209 (01) : 274 - 336
[3] Adler-Gelfand-Dickey Approach to Classical W-Algebras Within the Theory of Poisson Vertex Algebras
De Sole, Alberto
Kac, Victor G.
Valeri, Daniele
[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2015, 2015 (21) : 11186 - 11235
[4] Dirac Reduction for Poisson Vertex Algebras
De Sole, Alberto
Kac, Victor G.
Valeri, Daniele
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2014, 331 (03) : 1155 - 1190
[5] Non-local Poisson structures and applications to the theory of integrable systems
De Sole, Alberto
Kac, Victor G.
[J]. JAPANESE JOURNAL OF MATHEMATICS, 2013, 8 (02): : 233 - 347
[6] HAMILTONIAN THEORY OVER NONCOMMUTATIVE RINGS AND INTEGRABILITY IN MULTIDIMENSIONS
DORFMAN, IY
FOKAS, AS
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 1992, 33 (07) : 2504 - 2514
[7] FADDEEV LD, 1986, HAMILTONIAN APPROACH
[8] Kac V. G., 1998, Vertex Algebra for Beginners
[9] Kupershmidt B.A., 2000, MATH SURVEYS MONOGR, V78
[10] SIMPLE-MODEL OF INTEGRABLE HAMILTONIAN EQUATION
MAGRI, F
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 1978, 19 (05) : 1156 - 1162

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