Algebraic Structures in Extended Geometry

Artikel i vetenskaplig tidskrift, 2018

Extended geometry is a unifying framework including exceptional field theory (XFT) and double field theory (DFT). It gives a geometric underpinning of the duality symmetries of M-theory. In this talk I give an overview of the surprisingly rich algebraic structures which naturally appear in the context of extended geometry. This includes Borcherds superalgebras, Cartan type superalgebras (tensor hierarchy algebras) and L-infinity algebras. This is the written version of a talk based mainly on [1-6], presented at SQS 2017, Dubna, Aug. 2017.