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△-tame quasi-hereditary algebras
作者姓名:Yun-ge XU & Ying-bo ZHANG Faculty of Mathematics and Computer Science  Hubei University  Wuhan  China  School of Mathematics Sciences  Beijing Normal University  Beijing  China
作者单位:Yun-ge XU & Ying-bo ZHANG Faculty of Mathematics and Computer Science,Hubei University,Wuhan 430062,China; School of Mathematics Sciences,Beijing Normal University,Beijing 100875,China
基金项目:This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 10426014,10501010 and 19331030),the Foundation of Hubei Provincial Department of Education (Grant No.D200510005).
摘    要:Let (K, M,H) be an upper triangular bimodule problem. Briistle and Hille showed that the opposite algebra A of the endomorphism algebra of a projective generator P of the matrices category of (K., M, H) is quasi-hereditary, and there is an equivalence between the category of△-good modules of A and Mat(K, M). In this note, based on the tame theorem for bimodule problems, we show that if the algebra A associated with an upper triangular bimodule problem is of△-tame representation type, then the category F(△) has the homogeneous property, i.e. almost all modules in F(△) are isomorphic to their Auslander-Reiten translations. Moreover, if (K, M,H)is an upper triangular bipartite bimodule problem, then A is of△-tame representation type if and only if F(△) is homogeneous.

关 键 词:bimodule  problem    quasi-hereditary  algebra  △-tameness    homogeneity.
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