Hopf双Ore扩张的余乘和对极  

The comultiplications and antipodes of Hopf double Ore extensions

作　　者：雷思佳 沈远 LEI Sijia;SHEN Yuan(School of Science,Zhengjiang Sci-Tech University,Hangzhou 310018,China)

机构地区：[1]浙江理工大学理学院,杭州310018

出　　处：《浙江理工大学学报（自然科学版）》2022年第6期941-949,共9页Journal of Zhejiang Sci-Tech University(Natural Sciences)

基　　金：国家自然科学基金项目(11701515)。

摘　　要：为丰富Hopf代数的构造方法以及获得更多Hopf代数实例,引入一般的Hopf(右)双Ore扩张,刻画该扩张的Hopf代数结构。通过余结合性、余单位性和次数的对比,得到Hopf(右)双Ore扩张余乘应具有的3种形式;利用对极是反代数同态,获得Hopf(右)双Ore扩张对极的形式。结果表明:Hopf(右)双Ore扩张中添加的变量在余乘与对极作用下均不包含二元多项式,具有较为简洁的形式。该结果可为后续Hopf代数构造提供帮助。In order to enrich construction methods for Hopf algebras and obtain more examples of Hopf algebras, the general Hopf(right) double Ore extension is proposed. We aim to describe the Hopf structure of this kind of extensions. We show that there are three cases of the comultiplications of Hopf(right) double Ore extensions by coassociativity, counit and an argument of degrees. Using the fact that any antipode is an anti-algebra homomorphism, we obtain the form of the antipodes of Hopf(right) double Ore extensions. The results show that comultiplication and antipode acting on two new indeterminates of(right) double Ore extensions have concise forms which do not involve polynomials in two variables. The result is helpful for construction of Hopf algebras.

关 键 词：HOPF代数 双Ore扩张 Hopf双Ore扩张 余乘 对极 

分 类 号：O153.3[理学—数学]