外三角范畴粘合的低阶K-群

doi:10.6040/j.issn.1671-9352.0.2024.114

《山东大学学报(理学版)》 ›› 2026, Vol. 61 ›› Issue (4): 25-36.doi: 10.6040/j.issn.1671-9352.0.2024.114

• • 上一篇

外三角范畴粘合的低阶K-群

郑敏^1,2,陈清华^2*

1.福建江夏学院数理教研部, 福建福州 350108;2.福建师范大学数学与统计学院, 福建福州 350117

发布日期:2026-04-08
通讯作者: 陈清华(1962— ),男,教授,博士,研究方向为代数表示论. E-mail:cqhmath@fjnu.edu.cn
作者简介:郑敏(1983— ),女,副教授,博士,研究方向为代数表示论. E-mail:woshizhengmin20@163.com*通信作者:陈清华(1962— ),男,教授,博士,研究方向为代数表示论. E-mail:cqhmath@fjnu.edu.cn
基金资助:
国家自然科学基金资助项目(11871404);福建江夏学院国家基金培育项目(JXZ2023005)

Lower K-groups of the recollement of extriangulated categories

ZHENG Min^1,2, CHEN Qinghua^2*

1. Department of Mathematics and Physics, Fujian Jiangxia University, Fuzhou 350108, Fujian, China;
2. School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350117, Fujian, China

Published:2026-04-08

摘要/Abstract

摘要： 证明在一定条件下外三角范畴左(右)粘合中3个范畴的K_i-群间具有直和同构关系,推广关于Abel范畴(三角范畴)粘合的K_i-群的已有结论(i=0,1)。利用外三角范畴的粘合刻画3个范畴的幂等完备化范畴K_i-群的可加性(i=0,1)。

关键词: 外三角范畴, 粘合, K_i-群, 幂等完备化范畴, 三角范畴

Abstract: This paper proves that, under certain conditions, there exists the direct and isomorphic relation among the K_i-groups of three categories in the left(right)recollement of extriangulated categories, which generalizes the conclusions of K_i-groups of recollements of abelian(triangulated)categories(i=0,1). The recollement of extriangulated categories is used to describe the additivity of K_i-groups of the idempotent completion categories of its three categories(i=0,1).

Key words: extriangulated category, recollement, K_i-group, idempotent completion category, triangulated category

中图分类号:

O154

郑敏,陈清华. 外三角范畴粘合的低阶K-群[J]. 《山东大学学报(理学版)》, 2026, 61(4): 25-36.

ZHENG Min, CHEN Qinghua. Lower K-groups of the recollement of extriangulated categories[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2026, 61(4): 25-36.

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外三角范畴粘合的低阶K-群

Lower K-groups of the recollement of extriangulated categories

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