turkmath.org

Recent advancements in the mathematics of dualities seem to be in favor of certain generalizations of differential geometric structures on algebroids. The success of the generalized geometry program for T-duality motivates the construction of analogous exceptional geometries suitable for U-duality. In particular the Drinfeld double structure for Lie bialgebroids is a crucial concept for T-duality. In this talk, we will introduce the notion of bialgebroid extending these ideas in the realm of U-duality. We will present a calculus framework on algebroids; both twistless and twistful cases. In order to focus on exceptional geometries, we extend T-duality notions in a more general class of algebroids, where the setting allows us to work with non-dual vector bundles of arbitrary rank. We will conclude the talk with a specific construction crucial for exceptional Drinfeld algebras in the context of higher Courant algebroids and Nambu-Poisson structure.