English

Lie-Nijenhuis bialgebroids

Symplectic Geometry 2023-05-05 v1 Differential Geometry

Abstract

We introduce Lie-Nijenhuis bialgebroids as Lie bialgebroids endowed with an additional derivation-like object. They give a complete infinitesimal description of Poisson-Nijenhuis groupoids, and key examples include Poisson-Nijenhuis manifolds, holomorphic Lie bialgebroids and flat Lie bialgebra bundles. To achieve our goal we develop a theory of "generalized derivations" and their duality, extending the well-established theory of derivations on vector bundles.

Keywords

Cite

@article{arxiv.2004.10900,
  title  = {Lie-Nijenhuis bialgebroids},
  author = {Thiago Drummond},
  journal= {arXiv preprint arXiv:2004.10900},
  year   = {2023}
}

Comments

First version, 30 pages

R2 v1 2026-06-23T15:02:30.292Z