一类代数扩张与其模范畴

A Class Extension of an Algebra and its Category of Modules

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.

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, f）, 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） - rood which is isomorphic toT（A, I） -rood. 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.