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
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)=Dc(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)=Dc(A), if A is a Koszul connected cochain DG algebra such that H(A) is a Noetherian graded algebra with a balanced dualizing complex.
同调光滑DG代数 / Koszul DG代数 / 紧致DG模 / DG自由class {{custom_keyword}} /
homologically smooth DG algebra / Koszul DG algebra / DG free class / compact DG module {{custom_keyword}} /
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国家自然科学基金资助项目(11001056)
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