Quasi-Lie bialgebroids, Dirac structures and deformations of Poisson quasi-Nijenhuis manifolds

Abstract

We show how to deform a Poisson quasi-Nijenhuis manifold by means of a closed 2-form. Then we interpret this procedure in the context of quasi-Lie bialgebroids, as a particular case of the so called twisting of a quasi-Lie bialgebroid. Finally, we frame our result in the setting of Courant algebroids and Dirac structures.

arXiv comment17 pages

References in corpus (7)

• Nijenhuis Geometry
• Poisson Quasi-Nijenhuis Manifolds
• Lie theory of multiplicative tensors
• Poisson quasi-Nijenhuis structures with background
• Dirac structures and Nijenhuis operators
• Poisson quasi-Nijenhuis manifolds and the Toda system
• Reduction and construction of Poisson quasi-Nijenhuis manifolds with background