环自同构诱导的广义循环矩阵  

Generalized Circulant Matrices Related to Automorphisms

作　　者：徐华博 王利萍 XU Huabo;WANG Liping(School of Science,Beijing University of Civil Engineering and Architecture,Beijing 102616,China)

机构地区：[1]北京建筑大学理学院,北京102616

出　　处：《数学年刊(A辑)》2024年第4期423-436,共14页Chinese Annals of Mathematics

基　　金：北京市青年拔尖人才项目(No.21351918007);北京建筑大学研究能力提升计划(No.X22026)的资助。

摘　　要：设φ是结合环R上阶为n的自同构映射.根据自同构φ,作者引入广义循环矩阵的概念.令R^(φ)是R关于φ的不动点子环,C_(n)(φ,R)为R上所有n×n广义循环矩阵构成的集合.作者证明了C_(n)(φ,R)是自同态环EndR^(φ)(R^(n))的子环.此外,还证明了如果R是R^(φ)上交换的Hopf代数,则C_(n)(φ,R)也是R^(φ)上的Hopf代数.The authors introduce the definition of generalized circulant matrices which is the generalization of circulant matrices.Let R be an associative ring with an automorphismφof order n.They consider the set C_(n)(φ,R)of all the generalized circulant n×n matrices over R for any positive integer n.It is shown that C_(n)(φ,R)is a subring of the endomorphism ring of the R^(φ)-module R^(n),where R^(φ)is the invariant subring of R with respect toφ.Moreover,if R is a commutative Hopf algebra over R^(φ),then C_(n)(φ,R)is also a Hopf algebra over R^(φ).

关 键 词：广义循环矩阵 HOPF代数 不动点子环 

分 类 号：O15[理学—数学]