Roots of the affine Cremona group

Let k[x_1,…,x_n] be the polynomial algebra in n variables and let A^n=Spec k[x_1,…,x_n]. In this note we show that the root vectors of the affine Cremona group Aut(A^n) with respect to the diagonal torus are exactly the locally nilpotent derivations x^a\times d/dx_i, where x^a is any monomial not depending on x_i. This answers a question due to Popov.