# Crochets de Poisson gradués et applications: structures compatibles et généralisations des structures hyperkählériennes

@inproceedings{Antunes2010CrochetsDP, title={Crochets de Poisson gradu{\'e}s et applications: structures compatibles et g{\'e}n{\'e}ralisations des structures hyperk{\"a}hl{\'e}riennes}, author={Paulo Antunes}, year={2010} }

On trouve sur la plateforme de theses en ligne le resume suivant : "L'un des objets principaux de la these est de montrer que de nombreuses structures algebriques (algebroides de Lie, bigebroides de Lie, crochet de Schouten-Nijenhuis, crochet de Frolicher-Nijenhuis, etc. . . ), definies sur un fibre vectoriel A, s'expriment simplement en termes d'une structure de Poisson canonique, appelee le grand crochet, definie sur une certaine supervariete symplectique. On donne, par exemple, une formule…

## 14 Citations

Hierarchies and compatibility on Courant algebroids

- Mathematics
- 2011

We extend to the context of Courant algebroids several hierarchies that can be constructed on Poisson-Nijenhuis manifolds. More precisely, we introduce several notions (Poisson-Nijenhuis,…

Nijenhuis structures on Courant algebroids

- Mathematics
- 2011

We study Nijenhuis structures on Courant algebroids in terms of the canonical Poisson bracket on their symplectic realizations. We prove that the Nijenhuis torsion of a skew-symmetric endomorphism N…

Hypersymplectic structures on Courant algebroids

- Mathematics
- 2014

We introduce the notion of hypersymplectic structure on a Courant algebroid and we prove the existence of a one-to-one correspondence between hypersymplectic and hyperk\"ahler structures. This…

Nijenhuis forms on $L_\infty$-algebras and Poisson geometry

- Mathematics
- 2013

We investigate Nijenhuis deformations of $L_\infty$-algebras, a notion that unifies several Nijenhuis deformations, namely those of Lie algebras, Lie algebroids, Poisson structures and Courant…

? ? ( ? ? ) ? ? – ? ? c © ? ? Heldermann Verlag Version of April 4 , 2019 Homotopy equivalence of shifted cotangent bundles

- Mathematics
- 2019

Given a bundle of chain complexes, the algebra of functions on its shifted cotangent bundle has a natural structure of a shifted Poisson algebra. We show that if two such bundles are homotopy…

Compatibility on Courant algebroids

- Mathematics
- 2010

A Courant algebroid structure on a vector bundle E equipped with a fiberwise symmetric bilinear form 〈., .〉 is a pair (ρ, [., .]), where the anchor ρ is a bundle map from E to TM and the Dorfman…

Homotopy equivalence of shifted cotangent bundles

- Mathematics
- 2018

Given a bundle of chain complexes, the algebra of functions on its shifted cotangent bundle has a natural structure of a shifted Poisson algebra. We show that if two such bundles are homotopy…

Hyperstructures on Lie Algebroids

- Mathematics
- 2013

We define hypersymplectic structures on Lie algebroids recovering, as particular cases, all the classical results and examples of hypersymplectic structures on manifolds. We prove a 1-1…

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