English

Courant-Nijenhuis algebroids

Differential Geometry 2023-08-09 v1 Symplectic Geometry

Abstract

We introduce Courant 1-derivations, which describe a compatibility between Courant algebroids and linear (1,1)-tensor fields and lead to the notion of Courant-Nijenhuis algebroids. We provide examples of Courant 1-derivations on exact Courant algebroids and show that holomorphic Courant algebroids can be viewed as special types of Courant-Nijenhuis algebroids. By considering Dirac structures, one recovers the Dirac-Nijenhuis structures previously studied by the authors (in the special case of the standard Courant algebroid) and obtains an equivalent description of the Lie-Nijenhuis bialgebroids introduced by the second author via Manin triples.

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Cite

@article{arxiv.2305.03131,
  title  = {Courant-Nijenhuis algebroids},
  author = {Henrique Bursztyn and Thiago Drummond and Clarice Netto},
  journal= {arXiv preprint arXiv:2305.03131},
  year   = {2023}
}

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23 pages