# セミナー

## 微分幾何・トポロジーセミナー

タイトル Poisson Algebras Associated to Twisted Dirac Structures and Extended Symmetries 2013年6月3日 16：30～17：30 Alex Cardona (University of Los Andes) 慶應義塾大学理工学部　14棟733 In this talk we define Poisson algebras of admissible functions associated to Dirac structures twisted by a background 3-form and we will recall the standard cases associated to Dirac structures defined by graphs of non-degenerate 2-forms and other natural examples. We will also present the relationship between the extended symmetries of exact Courant algebroids over a manifold, the Poisson algebras of admissible functions associated to twisted Dirac structures when acted by Lie groups and Dirac reduction. We will show that the usual homomorphisms of Lie algebras between the algebras of infinitesimal symmetries of the action, vector fields on the manifold and the Poisson algebra of observables (appearing in symplectic geometry) generalize to natural maps of Leibniz algebras induced both by the extended action and compatible moment maps associated to it in the context of twisted Dirac structures.