Serre商范畴的Auslander-Reiten序列

Auslander-Reiten Sequences of Serre Quotient Categories

设A是有限维k-代数,A=A-mod,B是A的有厚度子范畴,通过从A的Auslander-Reiten(AR)序列到导出范畴Db(A)的AR三角的转化,研究A的AR序列与Serre商范畴A/B的AR序列的关系.文中给出A的AR序列在商函子Q∶A→A/B下的像是A/B的AR序列的充要条件.

Let A be a finite dimensional k-algebra, A be the category of finitely generated A-modules and B be a thick subcategory of A This paper mainly discusses the relationship between the Auslander-Reiten （AR） sequences of A and A/B by transforming the AR-sequences of A to the AR-triangles of the bounded derived category of A. We get some nec-essary and sufficient conditions that the AR-sequences of A/B are induced by the AR-sequences of A.