Unified tame theorem  

作　　者：ZHANG YingBo XU YunGe 

机构地区：[1]School of Mathematical Sciences,Beijing Normal University,Beijing 100875,China [2]School of Mathematics and Computer Science,Hubei University,Wuhan 430062,China

出　　处：《Science China Mathematics》2009年第9期2036-2068,共33页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos.10731070,10501010)

摘　　要：The well-known tame theorem tells that for a given tame bocs and a positive integer n there exist finitely many minimal bocses, such that any representation of the original bocs of dimension at most n is isomorphic to the image of a representation of some minimal bocses under a certain reduction functor. In the present paper we will give an alternative statement of the tame theorem in terms of matrix problem, by constructing a unified minimal matrix problem whose indecomposable matrices cover all the canonical forms of the indecomposable representations of dimension at most n for each non-negative integer n.The well-known tame theorem tells that for a given tame bocs and a positive integer n there exist finitely many minimal bocses, such that any representation of the original bocs of dimension at most n is isomorphic to the image of a representation of some minimal bocses under a certain reduction functor. In the present paper we will give an alternative statement of the tame theorem in terms of matrix problem, by constructing a unified minimal matrix problem whose indecomposable matrices cover all the canonical forms of the indecomposable representations of dimension at most n for each non-negative integer n.

关 键 词：matrix problem canonical form representation tame type INDECOMPOSABLE 15A21 16G20 16G60 16G70 

分 类 号：O151.2[理学—数学]