Seminar: Keremcan Doğan - Exceptional Drinfel’d Algebroids and Rackoids (May 15, 2026)

Speaker: Keremcan Doğan (Gebze Technical University)

Title: Exceptional Drinfel’d Algebroids and Rackoids

Time: May 15, 2026 at 13:30

Place: Feza Gürsey Center for Physics and Mathematics

Abstract:

String and M-theories dictate new symmetry notions that are absent in point-particle theories. The generalized geometry program extends usual differential geometry in a suitable manner to explain one class of these new symmetries, known as T-duality. In particular, Poisson-Lie T-duality can be understood as arising from different decompositions of the Drinfel’d double of a Lie bialgebra, which is itself a Lie algebra.

Extending this to the algebroid setting leads to Drinfel’d doubles of Lie bialgebroids, which are Courant algebroids. In order to explain another class of new symmetries, called U-duality, one needs to further extend these notions. In one of our recent works, we extended Lie bialgebroids and their Drinfel’d doubles to a set-up in which the vector bundles are not dual in the usual sense, and we introduced bialgebroids and their Drinfel’d doubles via a calculus framework on algebroids.

In this talk, we use this framework to introduce and construct a specific type of algebroid, which we call exceptional Drinfel’d algebroids. We prove that these are algebroid versions of exceptional Drinfel’d algebras, which have recently been defined in the physics literature in order to extend the Lie bialgebra/T-duality relation to the U-duality case; hence the name.

We provide a mathematically rigorous framework to describe these algebras and their algebroid versions in a frame-independent manner, where we use Nambu-Poisson structures and their certain generalizations. Moreover, we introduce exceptional Drinfel’d rackoids, which are global versions of exceptional Drinfel’d algebroids, analogous to the relation between a Lie group and its Lie algebra.

As examples, we focus on the SL(5) and E₆(₆) cases; for the latter we also use another extension called proto bialgebroids, where H- and R-fluxes are present.