【摘要】 对一已知代数进行扩张,并研究扩张代数、重复代数与其模范畴之间的关系.首先利用代数A的双边理想I构造扩张代数T(A,I)和重复代数T(A,I),并研究其模范畴;其次研究范畴T(A,I)-Mod与T(A,I)-Mod的关系,得到于T~v(A,I)-Mod同构于T(A,I)-mod;另外证明存在T(A,I)-mod到T(A,I)-mod的覆盖函子;最后研究商代数A/I的平凡扩张代数T(A/I),得出T(A/I)/I与扩张代数T(A,I)同构.更多还原

【Abstract】 This paper extends a known algebra and studies the relationship between algebra its extension algebra and repeated module category.Firstly,ideal T(A,I) of algebraic T(A,I),is used to construct extension algebra T(A,I),and the repetitive algebra T(A,I)- Mod whose module of two categories is studied.Secondly the relationship between category T(A,I)-Mod and category T(A,I)- mod is studied to generate T(A,I)- mod which is isomorphic toT(A,I)- mod.Thirdly,the existence of covering functorA/I toT(A/I) is proved.Finally,the trivial extension algebra T(A/I)/I is studied and the conclusion that the algebra T(A,I)is isomorphic to the expansion algebra is reached.更多还原