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