When the Schur functor induces a triangle-equivalence between Gorenstein defect categories  

作　　者：Huanhuan Li Jiangsheng Hu Yuefei Zheng 

机构地区：[1]School of Mathematics and Statistics,Xidian University,Xi'an 710071,China [2]School of Mathematics and Physics,Jiangsu University of Technology,Changzhou 213001,China [3]College of Science,Northwest A&F University,Yangling 712100,China

出　　处：《Science China Mathematics》2022年第10期2019-2034,共16页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 11626179, 12101474, 12171206 and 11701455);Natural Science Foundation of Jiangsu Province (Grant No. BK20211358);Natural Science Basic Research Plan in Shaanxi Province of China (Grant Nos. 2017JQ1012 and 2020JM-178);Fundamental Research Funds for the Central Universities (Grant Nos. JB160703 and 2452020182)。

摘　　要：Let R be an Artin algebra and e be an idempotent of R. Assume that Tor_(i)^(eRe)(Re, G) = 0 for any G ∈ GprojeRe and i sufficiently large. Necessary and sufficient conditions are given for the Schur functor S_(e) to induce a triangle-equivalence ■. Combining this with a result of Psaroudakis et al.(2014),we provide necessary and sufficient conditions for the singular equivalence ■ to restrict to a triangle-equivalence ■. Applying these to the triangular matrix algebra ■,corresponding results between candidate categories of T and A(resp. B) are obtained. As a consequence,we infer Gorensteinness and CM(Cohen-Macaulay)-freeness of T from those of A(resp. B). Some concrete examples are given to indicate that one can realize the Gorenstein defect category of a triangular matrix algebra as the singularity category of one of its corner algebras.

关 键 词：Schur functors triangle-equivalences singularity categories Gorenstein defect categories triangular matrix algebras 

分 类 号：O154.1[理学—数学]