DG - k -代数的Hochschild (Co)同调及其Koszul对偶

Pub Date : 2023-09-01 DOI:10.1007/s11464-020-0213-x

Yang Han, Xin Liu, Kai Wang

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引用次数: 0

摘要

我们比较了一个完全典型DG k -代数及其Koszul对偶的Hochschild (co)同调。证明了有限维完全典型对称DG - k代数的Koszul对偶是一个Calabi-Yau DG - k代数，其Hochschild上同调是Batalin-Vilkovisky代数。进一步证明了有限维完全典型对称DG - k代数及其Koszul对偶的Hochschild上同构为Batalin-Vilkovisky代数。

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Hochschild (Co)homologies of DG K-algebras and Their Koszul Duals

We compare the Hochschild (co)homologies of a complete typical DG K-algebra and its Koszul dual. We show that the Koszul dual of a finite dimensional complete typical symmetric DG K-algebra is a Calabi–Yau DG K-algebra whose Hochschild cohomology is a Batalin–Vilkovisky algebra. Furthermore, we prove that the Hochschild cohomologies of a finite dimensional complete typical symmetric DG K-algebra and its Koszul dual are isomorphic as Batalin–Vilkovisky algebras.

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