Loewy矩阵与几乎Koszul代数  

Loewy matrix and almost Koszul algebra

作　　者：罗德仁 吕天星 刘靓 LUO Deren;LU Tianxing;LIU Liang(School of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, China)

机构地区：[1]湖南理工学院数学学院,湖南岳阳414006

出　　处：《大连理工大学学报》2021年第4期436-440,共5页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(11901191);湖南省自然科学基金资助项目(2018JJ3204);湖南理工学院科研创新团队项目(2019-TD-15).

摘　　要：几乎Koszul代数作为Koszul代数的推广,在代数周期性和分次自入射代数的研究中起到了重要的作用.几乎Koszul代数的刻画是一个复杂的计算问题,而Loewy矩阵为Koszul代数的刻画带来了较为直观的计算方法.通过经典的Loewy矩阵和构造增广Loewy矩阵,利用分次代数分次模的两种不同Loewy维数向量得到了一个分次模成为d-线性模的充分必要条件,并得到了一个有限维分次代数成为几乎Koszul代数的充分必要条件,从而推广郭晋云利用Loewy矩阵刻画Koszul代数的相关结果.As a generalization of Koszul algebra,almost Koszul algebra plays an important role in the study of periodicity of algebras and graded self-injective algebras.The characterization of almost Koszul algebra is a complicated calculation problem,and the Loewy matrix brings a more intuitive calculation method to the characterization of Koszul algebra.Through the classical Loewy matrix and construction of the augmented Loewy matrix,using two different Loewy dimension vectors of graded modules of graded algebras,a sufficient and necessary condition is obtained for a graded module to become a d-linear module,and a sufficient and necessary condition is obtained for a finite-dimensional graded algebra to become an almost Koszul algebra.This generalizes the results of using Loewy matrix to characterize Koszul algebra of Guo Jinyun.

关 键 词：几乎Koszul代数 线性模 Loewy矩阵 Loewy维数向量 

分 类 号：O153.3[理学—数学]