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arXiv · 1604.02012

Poisson-Nijenhuis structures on quiver path algebras

Claudio Bartocci·Alberto Tacchella
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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].

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Claudio Bartocci, Alberto Tacchella. 2016-12-30. Poisson-Nijenhuis structures on quiver path algebras. https://doi.org/10.1007/s11005-017-0940-4

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