We prove that every derivation and every locally nilpotent derivation of the subalgebra K[xn, xn−1y, . . . , xyn−1, yn], where n ≥ 2, of the polynomial algebra K[x, y] in two variables over a field K of characteristic zero is induced by a derivation and a locally nilpotent derivation of K[x, y], respectively. Moreover, we prove that every automorphism of K[xn, xn−1y, . . . , xyn−1, yn] over an algebraically closed field K of characteristic zero is induced by an automorphism of K[x, y]. We also show that the group of automorphisms of K[xn, xn−1y, . . . , xyn−1, yn] admits an amalgamated free product structure.
Mathematics Subject Classification (2020): 14R10, 14J50, 13F20.