期刊论文

中文

重庆师范大学学报(自然科学版)

1672-6693

2017

34

1

69-72

10.11721/cqnuj20170110

No.2016JJ6049:国家自然科学基金 No.2016JJ624:国家自然科学基金

本校为其他机构

【目的】设$\Lambda $是一个连通的有限表示型的有限维自入射代数,$T\left(\Lambda \right)$是其平凡扩张代数。本研究主要目的是找出$\Lambda $的复杂度与$T$的复杂度之间的关系。【方法】首先当$\Lambda $是满足Fg假设的自入射代数时,$\Lambda $的表示维数大于等于$\Lambda $的复杂度加1,且有限表示型的表示维数等于2,所以$\Lambda $的复杂度小于等于1;又因为自入射代数$\Lambda $上的模的有无限投射维数,所以$\Lambda $的复杂度大于等于1,因而得到$\Lambda $的复杂度为1。其次,通过构造$T\left(\Lambda \right)$上单模的投射分解,具体计算$T\left(\Lambda \right)$上单模的投射分解中每一项$...

[Purposes] Let $\Lambda $ be a connected finite dimensional self-injective algebra of finite type,$T\left(\Lambda \right)$be its trivial extension. In this paper,we want to find out the relationship of the complexity between $\Lambda $ and its trivial extension $T\left(\Lambda \right)$. [Methods] Firstly if $\Lambda $ is the self-injective algebra satisfying Fgassumption,then the representation dimension of $\Lambda $ is one more than or equal to the complexity of $\Lambda $,and the representation dimension of algebra of finite representation type is 2,so the complexity of $\Lambda $ is less t...