  We apply the general formalism of nilpotent polynomials [Mandilara et al,
Phys. Rev. A 74, 022331 (2006)] to the problem of pure-state multipartite
entanglement classification in four qubits. In addition to establishing contact
with existing results, we explicitly show how the nilpotent formalism naturally
suggests constructions of entanglement measures invariant under the required
unitary or invertible class of local operations. A candidate measure of
fourpartite entanglement is also suggested, and its behavior numerically tested
on random pure states.
