论文标题
痕迹，舒伯特微积分和类别的Hochschild共同体$ \ Mathcal {O} $
Traces, Schubert calculus, and Hochschild cohomology of category $\mathcal{O}$
论文作者
论文摘要
我们讨论如何将DG类别的Hochschild共同体计算为其Serre函子的痕迹。将这种方法应用于伯恩斯坦（Gelfand）的主要区块 - gelfand-类别$ \ mathcal {o} $，我们获得了其Hochschild的共同体，作为相关空间的紧凑型共同体。同等地，将$ \ MATHCAL {O} $编写为模块的内态代数$ a $ a $ a $ a $ a $ toxpinive Generator，这是$ a $ a $的Hochschild共同体。特别是我们的计算给出了类型A中的$ \ Mathcal {O} $的Hochschild共同体的Euler特征。
We discuss how the Hochschild cohomology of a dg category can be computed as the trace of its Serre functor. Applying this approach to the principal block of the Bernstein--Gelfand--Gelfand category $\mathcal{O}$, we obtain its Hochschild cohomology as the compactly supported cohomology of an associated space. Equivalently, writing $\mathcal{O}$ as modules over the endomorphism algebra $A$ of a minimal projective generator, this is the Hochschild cohomology of $A$. In particular our computation gives the Euler characteristic of the Hochschild cohomology of $\mathcal{O}$ in type A.
