Fundamentals of quasigroup Hopf group-coalgebras  

拟群Hopf群余代数基本原理

作　　者：Zhang Senlin Wang Shuanhong 张森林;王栓宏(东南大学数学学院,南京211189)

机构地区：[1]School of Mathematics,Southeast University,Nanjing 211189,China

出　　处：《Journal of Southeast University(English Edition)》2021年第1期114-118,共5页东南大学学报（英文版）

基　　金：The National Natural Science Foundation of China(No.11371088,11571173,11871144);the Natural Science Foundation of Jiangsu Province(No.BK20171348).

摘　　要：A large class of algebras(possibly nonassociative)with group-coalgebraic structures,called quasigroup Hopf group-coalgebras,is introduced and studied.Quasigroup Hopf group-coalgebras provide a unifying framework for the classical Hopf algebras and Hopf group-coalgebras as well as Hopf quasigroups.Then,basic results similar to those in Hopf algebras H are proved,such as anti-(co)multiplicativity of the antipode S:H→H,and S^(2)=id if H is commutative or cocommutative.引入并研究一大类具有群余代数结构的(可能非结合的)代数族,称之为拟群Hopf群余代数.拟群Hopf群余代数为经典Hopf代数和Hopf群余代数以及Hopf拟群提供了统一的框架.接着,证明拟群Hopf群余代数中类似于Hopf代数理论中的基本结果.例如,Hopf代数理论中对极S:H→H的反(余)乘法性;如果H是交换的或余交换的,S^(2)=id.

关 键 词：Hopf quasigroup group-coalgebra quasigroup Hopf group-coalgebra convolution algebra 

分 类 号：O153[理学—数学]