# Dirac structures for generalized Lie bialgebroids

@article{Costa2004DiracSF, title={Dirac structures for generalized Lie bialgebroids}, author={J. M. Nunes da Costa and J. Clemente-Gallardo}, journal={Journal of Physics A}, year={2004}, volume={37}, pages={2671-2692} }

We study Dirac structures for generalized Courant algebroids, which are doubles of generalized Lie bialgebroids. The cases investigated include graphs of bivector fields and characteristic pairs of some sub-bundles.

## 21 Citations

Dirac pairs on Jacobi algebroids

- Mathematics
- 2021

We define Dirac pairs on Jacobi algebroids, which is a generalization of Dirac pairs on Lie algebroids introduced by Kosmann-Schwarzbach. We show the relationship between Dirac pairs on Lie and on…

On Quasi-Jacobi and Jacobi-Quasi Bialgebroids

- Mathematics
- 2006

We study quasi-Jacobi and Jacobi-quasi bialgebroids and their relationships with twisted Jacobi and quasi Jacobi manifolds. We show that we can construct quasi-Lie bialgebroids from quasi-Jacobi…

Dirac structures for generalized Courant and Courant algebroids

- Mathematics
- 2005

We establish some fundamental relations between Dirac subbundles $L$ for the generalized Courant algebroid $(A\oplus A^{\ast}, \phi+W)$ over a differentiable manifold $M$ and the associated Dirac…

Reduction of Poisson Manifolds and Jacobi Manifolds via Dirac Theory

- Mathematics
- 2011

We give two kinds of reduction relating Poisson manifolds and Jacobi manifolds by classifying reducible Dirac and Jacobi-Dirac structures into two classes, respectively. The proof needs only some…

Twisted cohomology of Lie algebroids

- Mathematics
- 2017

In this short note we define a new cohomology for a Lie algebroid A, that we call the twisted cohomology of A by an odd cocycle θ in the Lie algebroid cohomology of A. We proof that this cohomology…

Jacobi manifolds, Dirac structures and Nijenhuis operators

- Physics
- 2004

Research of J. M. Nunes da Costa supported by GRICES/French Embassy (Project 502 B2)
and CMUC-FCT

Gauge Transformations of Jacobi Structures and Contact Groupoids

- Mathematics, GeologyMathematical Physics, Analysis and Geometry
- 2019

We define gauge transformations of Jacobi structures on a manifold. This is related to gauge transformations of Poisson structures via the Poissonization. Finally, we discuss how the contact…

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