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.
作者
毛雪峰
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)
出处
《数学学报（中文版）》
CSCD
北大核心
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)
