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).
Poisson–Nijenhuis structures on quiver path algebras / Bartocci, C.; Tacchella, A.. - In: LETTERS IN MATHEMATICAL PHYSICS. - ISSN 0377-9017. - 107:7(2017), pp. 1265-1291. [10.1007/s11005-017-0940-4]
Poisson–Nijenhuis structures on quiver path algebras
Bartocci C.;Tacchella A.
2017-01-01
Abstract
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).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
