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.

引用

页码：377 / 395

页数：19

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