  In the late 1980s, Premet conjectured that the nilpotent variety of any
finite dimensional restricted Lie algebra over an algebraically closed field of
characteristic $p>0$ is irreducible. This conjecture remains open, but it is
known to hold for a large class of simple restricted Lie algebras, e.g. for Lie
algebras of connected reductive algebraic groups, and for Cartan series $W, S$
and $H$. In this paper, with the assumption that $p>3$, we confirm this
conjecture for the minimal $p$-envelope $W(1;n)_p$ of the Zassenhaus algebra
$W(1;n)$ for all $n\geq 2$.
