Premet proved the famous KW-conjecture in modular Lie algebra.
After, Premet introduced the finite $W$-algebra $U(g, e)$.
Also,  Premet proposed the conjecture every algebra $U(g, e)$ admits a $1$-dimensional
representation
then, Losev proved this conjecture for g classical.

so, a natural question,
for the super version, what about these results when we consider the basis classical Lie superalgebra,i.e, whether every super W-algebra admits a $1$-dim rep??


**EDIT**: Thanks for  Professor José Figueroa-O'Farrill pointing out that 
in the literature of mathematical physics, the finite
W-algebras appeared in the work of de Boer and Tjin from the viewpoint
of BRST quantum hamiltonian reduction.