| 同调光滑连通上链DG代数的一个注记 |
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| 引用本文： | 毛雪峰,谢建峰.同调光滑连通上链DG代数的一个注记[J].数学学报,2018,61(5):715-728. |
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| 作者姓名： | 毛雪峰 谢建峰 |
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| 作者单位： | 1. 上海大学数学系 上海 200444;
2. 喀什大学 喀什 844000 |
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| 基金项目： | 国家自然科学基金资助项目（11001056） |
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| 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D_(fg)(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D_(fg)(A)=D~c(A).
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A Note on Homologically Smooth Connected Cochain DG Algebras |
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| Xue Feng MAO,Jian Feng XIE.A Note on Homologically Smooth Connected Cochain DG Algebras[J].Acta Mathematica Sinica,2018,61(5):715-728. |
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| Authors: | Xue Feng MAO Jian Feng XIE |
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| Institution: | 1. Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China;
2. Kashgar University, Kashgar 844000, P. R. China |
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| Abstract: | 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. |
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| Keywords: | homologically smooth DG algebra Koszul DG algebra DG free class compact DG module |
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