Retractions and Gorenstein Homological Properties |
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Authors: | Xiao-Wu Chen Yu Ye |
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Institution: | 1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, Anhui, People’s Republic of China 2. Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences, Hefei, 230026, Anhui, People’s Republic of China
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Abstract: | 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′ such that there is a sequence of left retractions linking A to A′; in particular, the singularity category of A is triangle equivalent to the stable category of A′. We classify connected Nakayama algebras with at most three simple modules according to Gorenstein homological properties. |
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