A Nijenhuis operator on a manifold is a (1, 1) tensor whose Nijenhuis torsion vanishes. A Nijenhuis operator N determines a Lie algebroid that knows everything about N. In this sense, a Nijenhuis operator is an infinitesimal object. In this paper, we identify its global counterpart. Namely, we characterize Lie groupoids integrating the Lie algebroid of a Nijenhuis operator. We illustrate our integration result in various examples, including that of a linear Nijenhuis operator on a vector space or, which is equivalent, a pre-Lie algebra structure.
Integrating Nijenhuis structures
Pugliese F.;Sparano G.;Vitagliano L.
2023-01-01
Abstract
A Nijenhuis operator on a manifold is a (1, 1) tensor whose Nijenhuis torsion vanishes. A Nijenhuis operator N determines a Lie algebroid that knows everything about N. In this sense, a Nijenhuis operator is an infinitesimal object. In this paper, we identify its global counterpart. Namely, we characterize Lie groupoids integrating the Lie algebroid of a Nijenhuis operator. We illustrate our integration result in various examples, including that of a linear Nijenhuis operator on a vector space or, which is equivalent, a pre-Lie algebra structure.File in questo prodotto:
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