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数学进展 - 2018, Vol. 47(3): 393-400
研究论文
一类Koszul代数的$n$}-APR倾斜的$\tau_{[n]}$}-mutation实现
$n$}-APR Tilts of a Class of Koszul Algebra Realized by $\tau_{[n]}$}-mutations

罗德仁1, 张通亮2, 郑立景3,*
LUO Deren1, ZHANG Tongliang2, ZHENG Lijing3

1. 湖南理工学院数学学院, 岳阳, 湖南, 414000;
2. 湖南师范大学数学与计算机科学学院, ''高性能计算与随机信息处理''省部共建教育部重点实验室, 长沙, 湖南, 410006;
3. 南华大学数理学院, 衡阳, 湖南, 421001
1. College of Mathematics, Hunan Institute of Science and Technology, Yueyang,Hunan, 414000, P. R. China;
2. College of Mathematics and Computer Science, Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China), Hunan Normal University, Changsha, Hunan, 410006, P. R. China;
3. School of Mathematics and Physics, University of South China, Hengyang, Hunan, 421001, P. R. China

收稿日期: 2016-11-25
出版日期: 2018-06-08
2018, Vol. 47(3): 393-400
DOI: 10.11845/sxjz.2016137b


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摘要 本文引入一类Koszul代数的 $\tau_{[n]}$-mutation 的概念, 并证明对于整体维数小于等于$n$ 的Koszul 代数, 如果其Koszul对偶为允许$(n-1)$-平移代数, 则其$n$-APR 倾斜模的自同态代数的箭图可由其自身作$\tau_{[n]}$-mutation实现.
关键词 $n$-APR 倾斜模$n$-平移代数$\tau_{[n]}$-mutation    
Abstract:In this paper, we introduce the $\tau_{[n]}$-mutations of a class of Koszul algebra, and show that the $n$-APR tilts of Koszul algebra $\Lambda$ is $\tau_{[n]}$-mutation of $\Lambda$ if the global dimension $\Lambda\le n$ and the Koszul dual of $\Lambda$ is an admissable $(n-1)$-translation algebra.
Key words$n$-APR tilting module    $n$-translation algebra    $\tau_{[n]}$-mutation
PACS:  O154.2  
基金资助:国家自然科学基金(No. 11271119), 湖南省自然科学基金(Nos. 2016JJ6124, 2018JJ3204)和湖南省研究生创新项目(Nos. CX2013B216, CX2014B189).
通讯作者: E-mail: $*$ zhenglijing817@163.com   
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