  We prove that every derivation and every locally nilpotent derivation of the
subalgebra $K[x^n, x^{n-1}y,\ldots,xy^{n-1}, y^n]$, where $n\geq 2$, 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 $K[x^n,
x^{n-1}y,\ldots,xy^{n-1}, y^n]$ 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 $K[x^n, x^{n-1}y,\ldots,xy^{n-1}, y^n]$
admits an amalgamated free product structure.
