On locally nilpotent derivations of k[ X1, X2, Y]/( ϕ( Y)− X1X2)

Abstract

We investigate the locally nilpotent derivations of the k -algebra B= k [X 1,X 2,Y]/(ϕ−X 1X 2), where k is a field of characteristic zero, X 1, X 2, Y are indeterminates over k and ϕ∈ k [Y] is a nonconstant polynomial. We prove that a certain subgroup of Aut k (B) acts transitively on the set of kernels of nonzero locally nilpotent derivations of B.