A_(n)和D_(n)型箭图路代数的有界导出范畴的半倾斜对象  

Silting objects in bounded derived categories of path algebras of quivers of the types A_(n)and D_(n)

作　　者：陈伟钊 Weizhao Chen

机构地区：[1]上海交通大学数学科学学院,上海200240

出　　处：《中国科学：数学》2023年第1期3-24,共22页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:12131015,11971304)资助项目。

摘　　要：确定一个三角范畴的所有半倾斜对象,是一项基本且困难的问题.通过比较复杂的计算,对于A_(n)型箭图的路代数A,本文给出了确定A的有界导出范畴D^(b)(A)的所有半倾斜对象的法则.根据这个法则,当n给定时,理论上可以逐一写出D^(b)(A)的所有半倾斜对象.本文用有界同伦范畴K^(b)(proj A)不可分解的二项预半倾斜对象来描述这个法则.对于D_(n)型箭图的路代数A,本文也作了类似的研究.It is a basic and difficult problem to find all the silting objects of a triangulated category.In the case where A is a path algebra of quivers of the type A_(n),this paper gives rules of determining all the silting objects of the bounded derived category D^(b)(A),by which we can find all the silting objects of D^(b)(A)by complicated calculations when n is given.We describe these rules by using the indecomposable two-term presilting objects in K^(b)(proj A).For a path algebra of quivers of the type D_(n),we do some similar research.

关 键 词：半倾斜对象 预半倾斜对象 有界导出范畴 A_(n)型箭图 D_(n)型箭图 

分 类 号：O154.1[理学—数学]