同调光滑连通上链DG代数的一个注记  

A Note on Homologically Smooth Connected Cochain DG Algebras

作　　者：毛雪峰[1,2] 谢建峰 Xue Feng MAO;Jian Feng XIE(Department of Mathematics,Shanghai University,Shanghai 200444,P.R.China;Kashgar University,Kashgar 844000,P.R.China)

机构地区：[1]上海大学数学系,上海200444 [2]喀什大学,喀什844000

出　　处：《数学学报（中文版）》2018年第5期715-728,共14页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11001056)

摘　　要：本文给出了有关同调光滑连通上链微分分次（简称DG）代数的两个重要结论.具体地说,当A是同调光滑连通上链DG代数且其同调分次代数H（A）是诺特分次代数时,证明Dfg（A）中的任意Koszul DG A-模都是紧致的.另外,当A是Kozul连通上链DG代数且其同调分次代数H（A）是有平衡对偶复形的诺特分次代数时,证明A的同调光滑性质等价于Dfg（A） =D^c（A）.In this paper, we obtain two interesting results on homologically smooth connected cochain DG algebras. More precisely, we show that any Koszul DG A-module in Dfg（A） is compact, when A is a homologically smooth connected cochain DG algebra with a Noetherian cohomology graded algebra H（A）. We prove that the homologically smoothness of A is equivalent to Dfg（A） = D^c（A）, if A is a Koszul connected cochain DG algebra such that H（A） is a Noetherian graded algebra with a balanced dualizing complex.

关 键 词：同调光滑DG代数 KOSZUL DG代数 紧致DG模 DG自由class 

分 类 号：O154.2[理学—数学]