Nilpotent orbits in the Witt algebra W₁

In this article, the nilpotent orbits of the Witt algebra W₁ are determined under the automorphism group over an algebraically closed field F of characteristic p > 3. In contrast with a finite number of nilpotent orbits in a classical simple Lie algebra (cf. [5]), there is an infinite number of nilpotent orbits in W₁. A set of representatives of nilpotent orbits, as well as their dimensions, are precisely presented.