循环矩阵构成的Hopf代数  

Hopf Algebras on Circulant Matrices

作　　者：徐华博 XU Huabo(School of Science,Beijing University of Civil Engineering and Architecture,Beijing,100044,P.R.China)

机构地区：[1]北京建筑大学理学院,北京100044

出　　处：《数学进展》2021年第4期538-546,共9页Advances in Mathematics（China）

基　　金：Partially supported by Beijing Nova Program(No.Z181100006218010)。

摘　　要：C_(n)(R)表示交换环R上n阶循环矩阵的全体.根据通常矩阵的乘法∙和加法,C_(n)(R)同构于一个箭图代数.考虑矩阵的Hadamard积■,C_(n)(R)也为结合代数,在C_(n)(R)上定义了新的余乘Δ,余单位ε和对极S使得(C_(n)(R),■,μ,Δ,ε,S)做成Hopf代数.Let C_(n)(R)be the set of n×n circulant matrices over a commutative ring R.We show that the algebra C_(n)(R)defined in usual multiplication∙and addition is isomorphic to a quiver algebra.Meantime,C_(n)(R)is also an associative algebra under Hadamard product■.The new comultiplicationΔ,the counitεand an antipode S in C_(n)(R)are introduced such that(C_(n)(R),■,μ,Δ,ε,S)becomes a Hopf algebra.

关 键 词：循环矩阵 HOPF代数 箭图代数 

分 类 号：O153.3[理学—数学]