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arXiv · 2006.00237

Poisson-Nijenhuis Structure on Lie groupoids from the Invariance's Point of View

Gh. Haghighatdoost·J. Ojbag
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Abstract

In this paper, we introduce right-invariant (similarly, left-invariant) Poisson-Nijenhuis Structures on Lie groupoids and their infinitesimal counterparts as called $(Λ, \mathbf{n})-$structures. We present a mutual correspondence between $(Λ,\mathbf{n})-$structures on Lie algebroids with Poisson-Nijenhuis structures $(Π, \mathbf{N})$ on their Lie groupoids under some conditions. Also, we will construct Poisson-Nijenhuis pair groupoids as an example from the invariance's point of view.

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BibTeXRIS

Gh. Haghighatdoost, J. Ojbag. 2020-05-30. Poisson-Nijenhuis Structure on Lie groupoids from the Invariance's Point of View. https://arxiv.org/abs/2006.00237

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