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Let $\mathfrak{g}$ be a semisimple complex Lie algebra, and let $W$ be afinite subgroup of $\mathbb{C}$-algebra automorphisms of the enveloping algebra$U(\mathfrak{g})$. We show that the derived category of$U(\mathfrak{g})^W$-modules determines isomorphism classes of both$\mathfrak{g}$ and $W.$ Our proofs are based on the geometry of the Zassenhausvariety of the reduction modulo $p\gg 0$ of $\mathfrak{g}.$ Specifically, weuse non-existence of certain \'etale coverings of its smooth locus

Derived invariants of the fixed ring of enveloping algebras of semisimple Lie algebras