Algebraic structures in exceptional geometry

Abstract

Exceptional field theory (EFT) gives a geometric underpinning of the U-duality symmetries of M-theory. In this paper I give an overview of the surprisingly rich algebraic structures which naturally appear in the context of EFT. This includes Borcherds superalgebras, Cartan type superalgebras (tensor hierarchy algebras) and L∞ algebras. This is the written version of a talk based mainly on Refs. [1–6].