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

被引：0

作者：

Han, Yang ^{[1
,2
]}

Liu, Xin ^{[3
]}

Wang, Kai ^{[1
,2
]}

机构：

[1] Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China

[2] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

[3] RDFZ Chaoyang Sch, Beijing 100028, Peoples R China

来源：

FRONTIERS OF MATHEMATICS | 2023年 / 18卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Hochschild (co)homology; Koszul dual; symmetric DG K-algebra; Calabi-Yau DG K-algebra; Batalin-Vilkovisky (BV) algebra; BATALIN-VILKOVISKY ALGEBRAS; COHOMOLOGY; GERSTENHABER;

D O I：

10.1007/s11464-020-0213-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1113 / 1155

页数：43

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