On the semifree resolutions of DG algebras over the enveloping DG algebras

被引：0
|
作者：
Nasseh, Saeed [1 ]
Ono, Maiko [2 ]
Yoshino, Yuji [3 ]
机构：
[1] Georgia Southern Univ, Dept Math Sci, Statesboro, GA 30460 USA
[2] Okayama Univ Sci, Inst Advancement Higher Educ, Kitaku, Okayama 7000005, Japan
[3] Okayama Univ, Grad Sch Environm Life Nat Sci & Technol, Okayama, Japan
来源：
COMMUNICATIONS IN ALGEBRA | 2024年 / 52卷 / 02期
关键词：
Bar resolution; DG algebra; DG module; diagonal ideal; enveloping DG algebra; lifting; reduced bar resolution; semifree resolution; tensor algebra; universal derivation; WEAK LIFTINGS; EXTENSIONS;
D O I：
10.1080/00927872.2023.2247078
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The goal of this paper is to construct a semifree resolution for a non-negatively graded strongly commutative DG algebra B over the enveloping DG algebra B circle times AB, where A subset of B is a DG subalgebra and B is semifree over A. Our construction of such a semifree resolution, that we denote by (B,D), uses the notions of reduced bar resolution and tensor algebra of the shift of the diagonal ideal. As an application of (B,D), we provide a new characterization of naive liftability of semifree DG B-modules.
引用
收藏
页码：657 / 667
页数：11
相关论文
共 50 条
  • [1] DG-algebras and derived A∞-algebras
    Sagave, Steffen
    [J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2010, 639 : 73 - 105
  • [2] Compact DG modules and Gorenstein DG algebras
    Mao XueFeng
    Wu QuanShui
    [J]. SCIENCE IN CHINA SERIES A-MATHEMATICS, 2009, 52 (04): : 648 - 676
  • [3] Compact DG modules and Gorenstein DG algebras
    MAO XueFeng WU QuanShui School of Mathematical Sciences Fudan University Shanghai China
    [J]. ScienceinChina(SeriesA:Mathematics), 2009, 52 (04) : 648 - 676
  • [4] Compact DG modules and Gorenstein DG algebras
    MAO XueFeng & WU QuanShui School of Mathematical Sciences
    [J]. Science China Mathematics, 2009, (04) : 648 - 676
  • [5] Compact DG modules and Gorenstein DG algebras
    XueFeng Mao
    QuanShui Wu
    [J]. Science in China Series A: Mathematics, 2009, 52 : 648 - 676
  • [6] ASSOCIATED DG HOPF ALGEBRAS OF COMMUTATIVE ALGEBRAS
    CHEN, KT
    [J]. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 20 (03): : A357 - A358
  • [7] Homology over trivial extensions of commutative DG algebras
    Avramov, Luchezar L.
    Iyengar, Srikanth B.
    Nasseh, Saeed
    Sather-Wagstaff, Sean
    [J]. COMMUNICATIONS IN ALGEBRA, 2019, 47 (06) : 2341 - 2356
  • [8] Duality for cochain DG algebras
    Peter Jørgensen
    [J]. Science China Mathematics, 2013, 56 : 79 - 89
  • [9] Duality for cochain DG algebras
    Jorgensen, Peter
    [J]. SCIENCE CHINA-MATHEMATICS, 2013, 56 (01) : 79 - 89
  • [10] Duality for cochain DG algebras
    JφRGENSEN Peter
    [J]. Science China Mathematics, 2013, 56 (01) : 78 - 88
12345