Twisted Poisson Structures Research Articles

Relative modular classes of Lie algebroids

We study the relative modular classes of Lie algebroids, and we determine their relationship with the modular classes of Lie algebroids with a twisted Poisson structure. To cite this article: Y. Kosmann-Schwarzbach, A. Weinstein, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

Integration of twisted Poisson structures

Poisson manifolds may be regarded as the infinitesimal form of symplectic groupoids. Twisted Poisson manifolds considered by Ševera and Weinstein [Prog. Theor. Phys. Suppl. 144 (2001) 145] are a natural generalization of the former which also arises in string theory. In this note it is proved that twisted Poisson manifolds are in bijection with a (possibly singular) twisted version of symplectic groupoids.

Quasi-Lie Bialgebroids and Twisted Poisson Manifolds

We develop a theory of quasi-Lie bialgebroids using a homological approach. This notion is a generalization of quasi-Lie bialgebras, as well as twisted Poisson structures with a 3-form background which have recently appeared in the context of string theory, and were studied by Severa and Weinstein using a different method.

Poisson Geometry with a 3-Form Background

We study a modification of Poisson geometry by a closed 3-form. Just as for ordinary Poisson structures, these “twisted” Poisson structures are conveniently described as Dirac structures in suitable Courant algebroids. The additive group of 2-forms acts on twisted Poisson structures and permits them to be seen as glued from ordinary Poisson structures defined on local patches. We conclude with remarks on deformation quantization and twisted symplectic groupoids.