Retractions and Gorenstein Homological Properties

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• 作者：Xiao-Wu Chen (1) (2)
  Yu Ye (1) (2)
  
• 关键词：Retractions ; Gorenstein algebras ; Gorenstein projective modules ; Nakayama algebras ; CM ; free algebras ; 16G20 ; 16E50 ; 16D90
• 刊名：Algebras and Representation Theory
• 出版年：2014
• 出版时间：June 2014
• 年：2014
• 卷：17
• 期：3
• 页码：713-733
• 全文大小：
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• 作者单位：Xiao-Wu Chen (1) (2)
  Yu Ye (1) (2)
  
  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, Anhui, People鈥檚 Republic of China
  2. Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences, Hefei, 230026, Anhui, People鈥檚 Republic of China
  
• ISSN：1572-9079

文摘

We associate to a localizable module a left retraction of algebras; it is a homological ring epimorphism that preserves singularity categories. We study the behavior of left retractions with respect to Gorenstein homological properties (for example, being Gorenstein algebras or CM-free algebras). We apply the results to Nakayama algebras. It turns out that for a connected Nakayama algebra A, there exists a connected self-injective Nakayama algebra A鈥?such that there is a sequence of left retractions linking A to A鈥? in particular, the singularity category of A is triangle equivalent to the stable category of A鈥? We classify connected Nakayama algebras with at most three simple modules according to Gorenstein homological properties.