  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.
