[1]张梦蝶,刘雨喆,章 超*.Gentle代数的矩阵模型及其整体维数[J].江西师范大学学报(自然科学版),2023,(03):280-286.[doi:10.16357/j.cnki.issn1000-5862.2023.03.08]
　ZHANG Mengdie,LIU Yuzhe,ZHANG Chao*.The Matrix Model of Gentle Algebra and the Global Dimension[J].Journal of Jiangxi Normal University:Natural Science Edition,2023,(03):280-286.[doi:10.16357/j.cnki.issn1000-5862.2023.03.08]
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Gentle代数的矩阵模型及其整体维数()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2023年03期
页码:
280-286
栏目:
出版日期:
2023-05-25

文章信息/Info

Title:
The Matrix Model of Gentle Algebra and the Global Dimension
文章编号:
1000-5862(2023)03-0280-07
作者:
张梦蝶1; 刘雨喆2; 章 超1*
(1.贵州大学数学与统计学院,贵州 贵阳 550025; 2.南京大学数学系,江苏 南京 210093)
Author(s):
ZHANG Mengdie1;  LIU Yuzhe2;  ZHANG Chao1*
(1.School of Mathematics and Statistics, Guizhou University, Guiyang Guizhou 550025, China; 2.Department of Mathematics, Nanjing University, Nanjing Jiangsu 210093, China)
关键词:
投射模;  投射分解;  同调维数;  矩阵表示;  箭图表示
Keywords:
projective module;  projective resolution;  homological dimension;  matrix representation;  quiver representation.
分类号:
O 151.21; O 154.2
DOI:
10.16357/j.cnki.issn1000-5862.2023.03.08
文献标志码:
A
摘要:
该文利用Gentle代数的矩阵模型刻画了Gentle代数上的单模和投射模, 给出了单模的投射分解的矩阵表示. 由此指出Gentle代数的整体维数可以由它的矩阵模型所诱导的一类特殊子矩阵序列进行刻画. 并进一步指出这一类特殊子矩阵序列对应于Gentle代数的箭图上的极大非平凡Forbidden路, 从而得到Gentle代数的整体维数等于它的箭图上的极大非平凡Forbidden路的长度.
Abstract:
It is showed that for Gentle algebra, the simple module and projective module can be characterized by matrix model, and a matrix representation of projective resolution of simple module is provided. Thus the global dimension of a Gentle algebra can be characterized by a special submatrix sequence induced by its matrix model. Furthermore, by showing that above special submatrix sequences correspond to maximal non-trivial Forbidden paths on the quiver of Gentle algebra, the global dimension of Gentle algebra equals the length of the maximal nontrivial Forbidden path is obtained.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2022-11-10
基金项目:国家自然科学基金(11961007)和贵州省科学技术基金([2020]1Y405)资助项目.
通信作者:章 超(1986—),男,湖北宜昌人,教授,博士,主要从事基础数学(代数学)研究.E-mail:zhangc@amss.ac.cn
更新日期/Last Update: 2023-05-25