Matched pairs of Courant algebroids

  title={Matched pairs of Courant algebroids},
  author={Melchior Grutzmann and Mathieu Sti'enon},
  journal={Indagationes Mathematicae},
The standard cohomology of regular Courant algebroids
For any Courant algebroid E over a smooth manifold M with characteristic distribution F which is regular, we study the standard cohomology H• st(E) by using a special spectral sequence. We prove a
Atiyah class of a Manin pair
A Courant algebroid $E$ with a Dirac structure $L\subset E$ is said to be a Manin pair. We first discuss $E$-Dorfman connections on predual vector bundles $B$ and develop the corresponding Cartan
Dirac groupoids and Dirac bialgebroids
  • M. J. Lean
  • Mathematics
    Journal of Symplectic Geometry
  • 2019
We describe infinitesimally Dirac groupoids via geometric objects that we call Dirac bialgebroids. In the two well-understood special cases of Poisson and presymplectic groupoids, the Dirac
Linear generalised complex structures.
This paper studies linear generalised complex structures over vector bundles, as a generalised geometry version of holomorphic vector bundles. In an adapted linear splitting, a linear generalised
Poisson actions of Poisson Lie groups have an interesting and rich geometric structure. We will generalize some of this structure to Dirac actions of Dirac Lie groups. Among other things, we extend a
Gauge theory for string algebroids
We introduce a moment map picture for holomorphic string algebroids where the Hamiltonian gauge action is described by means of Morita equivalences, as suggested by higher gauge theory. The zero
Infinitesimal moduli for the Strominger system and generalized Killing spinors
We construct the space of infinitesimal variations for the Strominger system and an obstruction space to integrability, using elliptic operator theory. Motivated by physics, we provide refinements of
Canonical metrics on holomorphic Courant algebroids
Yau's solution of the Calabi Conjecture implies that every K\"ahler Calabi-Yau manifold $X$ admits a metric with holonomy contained in $\mathrm{SU}(n)$, and that these metrics are parametrized by the
On Dorfman connections of a Courant algebroid
We extend the Courant-Dorfman algebra of a Courant algebroid E to an algebra of differential operators on tensor products of E with values in tensor bundles of a vector bundle B, predual of E.


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
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