16 Sep 2025. Poster by Tom Ariel at the meeting of the Spanish Network of Geometry and Physics, Barcelona.
Abstract: Dirac structures are a geometric object generalizing symplectic and Poisson structures. From a physics viewpoint, they describe mechanical systems with both symmetries and constraints. Geometrically, they are given by subbundles of a vector bundle with additional structure, called a Courant algebroid. A pair of complementary Dirac structures in a Courant algebroid decomposes it as the double of a Lie bialgebroid. Our goal is to describe, in a given Courant algebroid, the obstruction to the existence of a Dirac complement for a given Dirac structure. Our main result provides an algebraic obstruction in terms of curved differential graded Lie algebras to the existence of a Dirac complement.