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arXiv · 2305.03131

Courant-Nijenhuis algebroids

Henrique Bursztyn·Thiago Drummond·Clarice Netto
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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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Henrique Bursztyn, Thiago Drummond, Clarice Netto. 2023-05-04. Courant-Nijenhuis algebroids. https://doi.org/10.1016/j.geomphys.2023.104923

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