Exceptional geometry and Borcherds superalgebras

TL;DR

This paper explores the algebraic structure of exceptional geometry's generalized diffeomorphisms using Borcherds superalgebras, revealing a unified and simplified framework for all cases with n less than 8.

Contribution

It introduces an extension of the Lie algebra e_n to an infinite-dimensional Borcherds superalgebra, providing a uniform algebraic description of generalized diffeomorphisms across different dimensions.

Findings

Generalized Lie derivatives are expressed uniformly for all n<8.

Closure of transformations follows from Jacobi identity and grading.

Extension to e_{n+1} simplifies the algebraic structure.

Abstract

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.