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

IF 0.8 3区数学 Q2 MATHEMATICS

Frontiers of Mathematics in China 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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来源期刊

Frontiers of Mathematics in China MATHEMATICS-

CiteScore

0.20

自引率

0.00%

发文量

703

审稿时长

6-12 weeks

期刊介绍： Frontiers of Mathematics in China provides a forum for a broad blend of peer-reviewed scholarly papers in order to promote rapid communication of mathematical developments. It reflects the enormous advances that are currently being made in the field of mathematics. The subject areas featured include all main branches of mathematics, both pure and applied. In addition to core areas (such as geometry, algebra, topology, number theory, real and complex function theory, functional analysis, probability theory, combinatorics and graph theory, dynamical systems and differential equations), applied areas (such as statistics, computational mathematics, numerical analysis, mathematical biology, mathematical finance and the like) will also be selected. The journal especially encourages papers in developing and promising fields as well as papers showing the interaction between different areas of mathematics, or the interaction between mathematics and science and engineering.