|本期目录/Table of Contents|

[1]周振强.Grothendieck范畴的斜群范畴[J].厦门大学学报(自然科学版),2018,57(04):532-535.[doi:10.6043/j.issn.0438-0479.201709008]
 ZHOU Zhenqiang.Skew Group Categories of Grothendieck Categories[J].Journal of Xiamen University(Natural Science),2018,57(04):532-535.[doi:10.6043/j.issn.0438-0479.201709008]
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《厦门大学学报(自然科学版)》[ISSN:0438-0479/CN:35-1070/N]

卷:
57卷
期数:
2018年04期
页码:
532-535
栏目:
研究论文
出版日期:
2018-07-31

文章信息/Info

Title:
Skew Group Categories of Grothendieck Categories
文章编号:
0438-0479(2018)04-0532-04
作者:
周振强
厦门理工学院应用数学学院,福建 厦门
Author(s):
ZHOU Zhenqiang
School of Applied Mathematics,Xiamen University of Technology,Xiamen 361024,China
关键词:
Grothendieck范畴 斜群范畴 余极限
Keywords:
Grothendieck category skew group category colimit
分类号:
O 154.1
DOI:
10.6043/j.issn.0438-0479.201709008
文献标志码:
A
摘要:
证明在群阶数|G|可逆的条件下,配备有限群G-作用的Grothendieck范畴C的斜群范畴C (G)是Grothendieck范畴.进一步地,若C还是局部有限生成(局部 Noether或局部有限表现)范畴,则C(G)亦是局部有限生成(局部 Noether或局部有限表现)范畴.
Abstract:
In this article,we prove that the skew group category C(G)of a Grothendieck category C with a finite group G-action is a Grothendieck category,under the condition that the order of the group is invertible in C.Furthermore,if C is a local finitely generated category(local finitely noetherian category or local finitely presented category respectively),then so is C(G).

参考文献/References:

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[2] GABRIEL P.Des catégories abéliennes[J].Bull Soc Math France,1962,90:323-448.
[3] REITEN I,RIEDTMANN C.Skew group algebras in the representation theory of artin algebras[J].J Algebra,1985,92:224-282.
[4] ZHOU Z.A note on skew group categories[J].Hokkaido Math J,2017,46(2):189-207.
[5] LIN Y,ZHOU Z.Tilted algebras and crossed products[J].Glasgow Mathematical Journal,2016,58:559-571.
[6] STENSTR?M B.Ring of quotients[M].Berlin-Heidelberg-New York:Springer-Verlag,1975:114-133.
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备注/Memo

备注/Memo:
收稿日期:2017-09-10 录用日期:2018-05-01
基金项目:国家自然科学基金(11701486,11626199); 厦门理工学院高层次人才引进项目(YKJ15032R)
Email:zhouzhenqiang2005@163.com
引文格式:周振强.Grothendieck范畴的斜群范畴[J].厦门大学学报(自然科学版),2018,57(4):532-535.
Citation:ZHOU Z Q.Skew group categories of grothendieck categories[J].J Xiamen Univ Nat Sci,2018,57(4):532-535.(in Chinese)
更新日期/Last Update: 1900-01-01