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 \( {\mathfrak{e}}_n \) to an infinite-dimensional Borcherds superalgebra, involving also the extension to \( {\mathfrak{e}}_{n+1} \), the generalized Lie derivatives can be expressed in a simple way, and the expressions take the same form for any n ≤ 7. The closure of the transformations then follows from the Jacobi identity and the grading of \( {\mathfrak{e}}_{n+1} \) with respect to \( {\mathfrak{e}}_n \).
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Palmkvist, J. Exceptional geometry and Borcherds superalgebras. J. High Energ. Phys. 2015, 32 (2015). https://doi.org/10.1007/JHEP11(2015)032
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DOI: https://doi.org/10.1007/JHEP11(2015)032