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[1]许东勃,林增强.线性平凡扩张范畴[J].厦门大学学报(自然科学版),2012,51(6):955.
 Trivial Extensions of k-linear Categories.Trivial Extensions of k-linear Categories[J].Journal of Xiamen University(Natural Science),2012,51(6):955.
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《厦门大学学报(自然科学版)》[ISSN:0438-0479/CN:35-1070/N]

卷:
51卷
期数:
2012年第6期
页码:
955
栏目:
研究论文
出版日期:
2012-11-30

文章信息/Info

Title:
Trivial Extensions of k-linear Categories
作者:
许东勃林增强
华侨大学数学科学学院, 福建 泉州 362021
Author(s):
Trivial Extensions of k-linear Categories
School of Mathematical Sciences,Huaqiao University,Quanzhou 362021,China
关键词:
平凡扩张范畴 三角矩阵范畴 模范畴
Keywords:
trivial extensions categories triangular matrix categories module categories
分类号:
O 153.3; O 154.1
文献标志码:
A
摘要:
Ck-线性范畴,MC-C双模,定义k-线性平凡扩张范畴C’=CM,首先证明其为平凡扩张代数的自然推广,其次证明左C’-模范畴等价于左C-模范畴关于张量函子MC-的右平凡扩张范畴(C-Mod)(MC-),推广了经典的平凡扩张代数的模范畴理论.并将此结论应用到k-线性三角矩阵范畴,重新刻画其模范畴的结构.
Abstract:
In this paper,the trivial extension of a k-linear category is introduced,which is a generalization of the trivial extension of an algebra.Let C’=CM be the trivial extension of a k-linear category C by a C-bimodule M.It is proved that the left module category C’-Mod is equivalent to the right trivial extension category(C-Mod)(MC-),which generalizes the classical theory on module category of trivial extensions of algebras.When,applying the above result to the k-linear triangular matrix category,it is easy to describe the structure of its module category.

参考文献/References:


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备注/Memo

备注/Memo:
收稿日期:2012-05-25
基金项目:国家自然科学基金项目(11126331,11101089)
更新日期/Last Update: 2012-11-20