Poisson-Nijenhuis structures on quiver path algebras
Mathematical Physics
2017-03-08 v2 math.MP
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 [3].
Keywords
Cite
@article{arxiv.1604.02012,
title = {Poisson-Nijenhuis structures on quiver path algebras},
author = {Claudio Bartocci and Alberto Tacchella},
journal= {arXiv preprint arXiv:1604.02012},
year = {2017}
}
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23 pages