一类合冲无限的自内射代数

doi:10.6040/j.issn.1671-9352.0.2023.391

《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (11): 115-121.doi: 10.6040/j.issn.1671-9352.0.2023.391

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一类合冲无限的自内射代数

周建国¹,刘雨喆^1*,章超¹,张亚峰²

1.贵州大学数学与统计学院, 贵州贵阳 550025;2.兰州财经大学信息工程学院, 甘肃兰州 730020

发布日期:2025-11-11
通讯作者: 刘雨喆(1992— ),男,讲师,博士,研究方向为代数表示论与同调代数. E-mail:liuyz@gzu.edu.cn
作者简介:周建国(1997— ),男,硕士研究生,研究方向为代数表示论与同调代数. E-mail:14785841291@163.com
基金资助:
国家自然科学基金资助项目(12171207,12061001);贵州大学引进人才科研启动基金资助项目(贵大人基合字(2022)53号,(2022)65号)

A syzygy-infinite self-injective algebras

ZHOU Jianguo¹, LIU Yuzhe^1*, ZHANG Chao¹, ZHANG Yafeng²

1. School of Mathematics and Statistics, Guizhou University, Guiyang 550025, Guizhou, China;
2. School of Information Engineering, Lanzhou University of Finance and Economics, Lanzhou 730020, Gansu, China

Published:2025-11-11

摘要/Abstract

摘要： 对于一个定义在代数闭域k上的有限维k-代数Λ,如果Λ是合冲有限的,则利用它是n-Igusa-Todorov代数,可知其有限维数有限。利用一类Nakayama代数的包络代数来指出该命题的逆不成立,即存在有限维数有限的代数,其合冲无限。

关键词: 箭图表示, 张量代数, 包络代数, 有限维数, 自内射维数

Abstract: Let Λ be a finite dimensional k-algebra with an algebraically closed field k. It is well-known that if Λ is syzygy-finite then, by using that Λ is an n-Igusa-Todorov algebra, its finitistic dimension is finite. This paper shows that the inverse of the above proposition is false by the enveloping algebra of some Nakayama algebras, that is, there exists an algebra with finite finitistic dimension such that it is a syzygy-infinite algebra.

Key words: quiver representation, tensor algebra, enveloping algebra, finitistic dimension, self-injective dimension

中图分类号:

O154

周建国,刘雨喆,章超,张亚峰. 一类合冲无限的自内射代数[J]. 《山东大学学报(理学版)》, 2025, 60(11): 115-121.

ZHOU Jianguo, LIU Yuzhe, ZHANG Chao, ZHANG Yafeng. A syzygy-infinite self-injective algebras[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(11): 115-121.

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一类合冲无限的自内射代数

A syzygy-infinite self-injective algebras

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