Exceptional geometry and Borcherds superalgebras

Understand

We study generalized diffeomorphisms in exceptional geometry with U-duality group E_{n(n)} from an algebraic point of view.

• By extending the Lie algebra e_n to an infinite-dimensional Borcherds superalgebra, involving also the extension to e_{n+1}, the generalized Lie derivatives can be expressed in a simple way, and the expressions take the same form for any n less than 8.
• The closure of the transformations then follows from the Jacobi identity and the grading of e_{n+1} with respect to e_n.