第二种Hochschild上同调：Koszul对偶与Morita不变性
Hochschild cohomology of the second kind: Koszul duality and Morita invariance
AI总结：
本文研究了第二种Hochschild上同调的定义、性质及其在Koszul对偶和Morita等价下的不变性，展示了其在不同范畴中的应用。
摘要：
我们定义了微分格（dg）或弯曲代数的第二种Hochschild上同调作为扭曲导出范畴中的导出函子，并证明其在适当的第二种Morita等价下是不变的。构造了双模版本的Koszul对偶，并利用其证明第二种Hochschild上同调在（非nilpotent）Koszul对偶下得以保持。我们证明了代数的第二种Hochschild上同调通常计算出几何上有意义的dg范畴的普通Hochschild上同调。例子包括拓扑空间上的无穷局部系统范畴、复代数流形的有界导出范畴以及矩阵因子化范畴。
英文摘要：
We define Hochschild cohomology of the second kind for differential graded (dg) or curved algebras as a derived functor in the twisted derived category. The Hochschild cohomology of the second kind of a curved or curved algebra $A$ is then equivalent to the classical Hochschild cohomology of the twisted derived dg category of $A$, which is often geometrically meaningful. Examples include the category of $\infty$-local systems on a topological space, the bounded derived category of a complex manifold and the category of matrix factorizations. We also show that Hochschild cohomology of the second kind is preserved under (nonconilpotent) Koszul duality and weak equivalences of curved algebras. The main technical ingredient is a new bimodule version of Koszul duality.
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