Poisson-Nijenhuis structures on quiver path algebras

被引：0

作者：

Bartocci, Claudio ^{[1
]}

Tacchella, Alberto ^{[1
]}

机构：

[1] Univ Genoa, Dipartimento Matemat, Via Dodecaneso 35, I-16146 Genoa, Italy

来源：

LETTERS IN MATHEMATICAL PHYSICS | 2017年 / 107卷 / 07期

关键词：

Quiver representations; Bihamiltonian structures; Integrable systems; Calogero-Moser system; NONCOMMUTATIVE SYMPLECTIC-GEOMETRY; YANG-MILLS THEORY; BIHAMILTONIAN STRUCTURES; INTEGRABLE SYSTEMS; DUALITY; MODEL;

D O I：

10.1007/s11005-017-0940-4

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We introduce a notion of noncommutative Poisson-Nijenhuis structure on the path algebra of a quiver. In particular, we focus on the case when the Poisson bracket arises from a noncommutative symplectic form. The formalism is then applied to the study of the Calogero-Moser and Gibbons-Hermsen integrable systems. In the former case, we give a new interpretation of the bihamiltonian reduction performed in Bartocci et al. (Int Math Res Not 2010:279-296, 2010. arXiv:0902.0953).

引用

页码：1265 / 1291

页数：27

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