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

中文翻译：

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半单李代数包络代数固定环的推导不变量

令 $${\mathfrak {g}}$$ g 是一个半单复李代数，让 W 是 $${\mathbb {C}}$$ C -包络代数 $$U 的代数自同构的有限子群({\mathfrak {g}})$$ U ( g ) 。我们证明 $$U({\mathfrak {g}})^W$$ U ( g ) W -modules 的派生范畴决定了 $${\mathfrak {g}}$$ g 和 W 的同构类。我们的证明基于 $$p\gg 0$$ p ≫ 0 of $${\mathfrak {g}}.$$ g 的归约模数的 Zassenhaus 变体的几何结构。具体来说，我们使用其平滑轨迹的某些 étale 覆盖的不存在。