Reducing Homological Conjectures by n-Recollements

被引：29
|
作者：
Qin, Yongyun [1 ]
Han, Yang [2 ]
机构：
[1] Qujing Normal Univ, Coll Math & Informat Sci, Qujing 655011, Yunnan, Peoples R China
[2] Chinese Acad Sci, KLMM, ISS, AMSS, Beijing 100190, Peoples R China
来源：
ALGEBRAS AND REPRESENTATION THEORY | 2016年 / 19卷 / 02期
基金：
中国国家自然科学基金;
关键词：
n-recollement; n-derived-simple algebra; Cartan determinant; Homologically smooth algebra; Gorenstein algebra; ALGEBRAIC K-THEORY; MODULE CATEGORIES; GLOBAL DIMENSION; CARTAN MATRIX; RINGS; LOCALIZATION; FUNCTORS;
D O I：
10.1007/s10468-015-9578-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
n-recollements of triangulated categories and n-derived-simple algebras are introduced. The relations between the n-recollements of derived categories of algebras and the Cartan determinants, homological smoothness and Gorensteinness of algebras respectively are clarified. As applications, the Cartan determinant conjecture is reduced to 1-derived-simple algebras, and the Gorenstein symmetry conjecture is reduced to 2-derived-simple algebras.
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页码：377 / 395
页数：19
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