Dimensions of triangulated categories with respect to subcategories

被引：12

作者：

Aihara, Takuma ^{[1
]}

Araya, Tokuji ^{[2
]}

Iyama, Osamu ^{[3
]}

Takahashi, Ryo ^{[3
,4
]}

Yoshiwaki, Michio ^{[5
]}

机构：

[1] Chiba Univ, Grad Sch Sci & Technol, Div Math Sci & Phys, Chiba 2638522, Japan

[2] Tokuyama Coll Technol, Liberal Arts Div, Shunan, Yamaguchi 7458585, Japan

[3] Nagoya Univ, Grad Sch Math, Chikusa Ku, Nagoya, Aichi 4648602, Japan

[4] Univ Nebraska, Dept Math, Lincoln, NE 68588 USA

[5] Osaka City Univ, Adv Math Inst, Sumiyoshi Ku, Osaka 5588585, Japan

来源：

JOURNAL OF ALGEBRA | 2014年 / 399卷

关键词：

Dimension of triangulated category; Functor category; Global dimension; Resolving subcategory; Cotilting module; Cohen-Macaulay module; REPRESENTATION THEORY; ARTIN ALGEBRAS; MODULES;

D O I：

10.1016/j.jalgebra.2013.09.035

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper introduces a concept of dimension of a triangulated category with respect to a fixed full subcategory. For the bounded derived category of an abelian category, upper bounds of the dimension with respect to a contravariantly finite subcategory and a resolving subcategory are given. Our methods not only recover some known results on the dimensions of derived categories in the sense of Rouquier, but also apply to various commutative and non-commutative noetherian rings. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：205 / 219

页数：15

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