# Poisson-Nijenhuis groupoids

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Apurba Das

created by lapastina on 22 Feb 2018

28 feb 2018
-- 11:00

UniversitÃ degli Studi di Salerno - Sala riunioni DipMat

**Abstract.**

A Poisson-Nijenhuis manifold is a Poisson manifold together with a Nijenhuis tensor which is compatible with the Poisson structure. In this talk we study multiplicative Poisson-Nijenhuis structure on a Lie groupoid which extends the notion of symplectic-Nijenhuis groupoid introduced by StiÃ©non and Xu. We also introduce a special class of Lie bialgebroid structures on a Lie algebroid A, called P-N Lie bialgebroids, which defines a hierarchy of compatible Lie bialgebroid structures on A. Next we show that under certain topological assumptions on a Lie groupoid, there is a one-to-one correspondence between multiplicative Poisson-Nijenhuis structures on it and P-N Lie bialgebroid structures on its Lie algebroid. Finally we define P-N action and indicate towards the notion of Morita equivalence of symplectic-Nijenhuis groupoids.