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
收藏
页码：1025 / 1099
页数：75
相关论文
共 15 条
  • [11] Integrable ODEs on associative algebras
    Mikhailov, AV
    Sokolov, VV
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2000, 211 (01) : 231 - 251
  • [12] Double Poisson brackets on free associative algebras
    Odesskii, Alexander
    Rubtsov, Vladimir
    Sokolov, Vladimir
    [J]. NONCOMMUTATIVE BIRATIONAL GEOMETRY, REPRESENTATIONS AND COMBINATORICS, 2013, 592 : 225 - +
  • [13] OLVER P, 1993, GRAD TEXTS MATH, V107, P36602
  • [14] Integrable evolution equations on associative algebras
    Olver, PJ
    Sokolov, VV
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1998, 193 (02) : 245 - 268
  • [15] Double Poisson algebras
    Van Den Bergh, Michel
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 360 (11) : 5711 - 5769
12