We classify all equivalences between the indecomposable abelian categories which appear as blocks in BGG category $${\mathcal {O}}$$ for reductive Lie algebras. Our classification implies that a block in category $${\mathcal {O}}$$ only depends on the Bruhat order of the relevant parabolic quotient of the Weyl group. As part of the proof, we observe that any finite dimensional algebra with simple preserving duality admits at most one quasi-hereditary structure.

中文翻译：

---

BGG 类别中块的分类 $${\mathcal {O}}$$ O

我们对还原李代数的 BGG 类别 $${\mathcal {O}}$$ 中显示为块的不可分解阿贝尔类别之间的所有等价物进行分类。我们的分类意味着 $${\mathcal {O}}$$ 类别中的块仅取决于 Weyl 群的相关抛物商的 Bruhat 阶数。作为证明的一部分，我们观察到任何具有简单保留对偶性的有限维代数最多允许一个准遗传结构。