△-tame quasi-hereditary algebras  

作　　者：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 

出　　处：《Science China Mathematics》2007年第2期240-252,共13页中国科学：数学（英文版）

基　　金：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.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. 

分 类 号：O153.4[理学—数学]