Abstract

Let k([n]) = k[x(1), ..., x(n)] be the polynomial algebra in n variables and let A(n) = Spec k([n]). In this note we show that the root vectors of Aut* (A(n)), the subgroup of volume preserving automorphisms in the a ffi ne Cremona group Aut(A(n)), with respect to the diagonal torus are exactly the locally nilpotent derivations x alpha (partial derivative/partial derivative x(i)), where x(alpha) is any monomial not depending on x(i). This answers a question posed by Popov.