Morita equivalence of Nijenhuis structures

TL;DR

This paper develops Morita equivalence concepts for Nijenhuis structures on groupoids and algebroids, linking global and infinitesimal perspectives and exploring invariance properties.

Contribution

It introduces Morita equivalence for Nijenhuis groupoids and algebroids, extending known results to include holomorphic cases and invariance of modular classes.

Findings

Established Morita equivalence for Nijenhuis groupoids and algebroids.

Connected global and infinitesimal structures via the Lie functor.

Proved invariance of the modular class of Poisson-Nijenhuis manifolds under Morita equivalence.

Abstract

We introduce Morita equivalence for Nijenhuis groupoids and for their infinitesimal counterparts, establishing a global-to-infinitesimal correspondence under the Lie functor. A special case is that of holomorphic Lie groupoids and algebroids. We use our framework to enhance the known Morita equivalences for quasi-symplectic groupoids and Dirac structures with compatible Nijenhuis structures. Finally, subject to certain conditions, we prove that the modular class of Poisson-Nijenhuis manifolds is invariant under Morita equivalence.