I need to prove that the Lie algebra defined as: $W_{n} = \operatorname{Der} \left(\mathbb F_p [x_1, \dots, x_n ] / (x_1^p, \dots, x_n^p )\right)$, when $(x_1^p, \dots, x_n^p )$ is the ideal generated from the monomials $x_1^p, \dots, x_n^p$ and when $p$ is prime, is simple.
I have tried following several strategies, such as taking a nontrivial ideal and trying to prove it will be all, but couldn't do it.
Also, I know that this Lie algebra is bounded, and I tried using this fact, but without success.
I would greatly appreciate any help!
Thanks.