{"title":"Hochschild (Co)homologies of DG K-algebras and Their Koszul Duals","authors":"Yang Han, Xin Liu, Kai Wang","doi":"10.1007/s11464-020-0213-x","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s11464-020-0213-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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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