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.
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)。
