Courant-Nijenhuis algebroids
arXiv:2305.03131 · doi:10.1016/j.geomphys.2023.104923
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.
arXiv comment23 pages
References in corpus (8)
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- Holomorphic Poisson Manifolds and Holomorphic Lie Algebroids
- Poisson Quasi-Nijenhuis Manifolds
- Lie theory of multiplicative tensors
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- Courant-Nijenhuis tensors and generalized geometries
- Dirac structures and Nijenhuis operators
- Nijenhuis and Compatible Tensors on Lie and Courant algebroids