Matched pairs of Courant algebroids

@article{Grutzmann2014MatchedPO,
  title={Matched pairs of Courant algebroids},
  author={Melchior Grutzmann and Mathieu Sti'enon},
  journal={Indagationes Mathematicae},
  year={2014},
  volume={25},
  pages={977-991}
}
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References

SHOWING 1-10 OF 19 REFERENCES
Matched pairs of Lie algebroids
  • T. Mokri
  • Mathematics
    Glasgow Mathematical Journal
  • 1997
Abstract We extend to Lie algebroids the notion variously known as a double Lie algebra (Lu and Weinstein), matched pair of Lie algebras (Majid), or twilled extension of Lie algebras
A construction of Courant algebroids on foliated manifolds
For any transversal-Courant algebroid E on a foliated manifold (M,F), and for any choice of a decomposition T M = TF © Q, we construct a
On Regular Courant Algebroids
For any regular Courant algebroid, we construct a characteristic class a la Chern-Weil. This intrinsic invariant of the Courant algebroid is a degree-3 class in its naive cohomology. When the Courant
Courant algebroids, derived brackets and even symplectic supermanifolds
In this dissertation we study Courant algebroids, objects that first appeared in the work of T. Courant on Dirac structures; they were later studied by Liu, Weinstein and Xu who used Courant
Remarks on the Definition of a Courant Algebroid
The notion of a Courant algebroid was introduced by Liu, Weinstein, and Xu in 1997. Its definition consists of five axioms and a defining relation for a derivation. It is shown that two of the axioms
Double Lie algebroids and second-order geometry, I
MATCHED PAIRS OF LIE GROUPS ASSOCIATED TO SOLUTIONS OF THE YANG-BAXTER EQUATIONS
Two groups G, H are said to be a matched pair if they act on each other and these actions, (a, /?), obey a certain compatibility condition. In such a situation one may form a bicrossproduct group,
Manin Triples for Lie Bialgebroids
In his study of Dirac structures, a notion which includes both Poisson structures and closed 2-forms, T. Courant introduced a bracket on the direct sum of vector fields and 1-forms. This bracket does
Dirac structures of integrable evolution equations
Holomorphic Poisson Manifolds and Holomorphic Lie Algebroids
We study holomorphic Poisson manifolds and holomorphic Lie algebroids from the viewpoint of real Poisson geometry. We give a characterization of holomorphic Poisson structures in terms of the Poisson
...
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