东南大学学报（英文版）2019，Vol.35Issue(4)：522-526,5.DOI:10.3969/j.issn.1003-7985.2019.04.016
Galois线性映射及其构造
Galois linear maps and their construction
摘要
Abstract
The condition of an algebra to be a Hopf algebra or a Hopf (co)quasigroup can be determined by the properties of Galois linear maps.For a bialgebra H,if it is unital and associative as an algebra and counital coassociative as a coalgebra,then the G-alois linear maps T1 and T2 can be defined.For such a bialgebra H,it is a Hopf algebra if and only if T1 is bijective.Moreover,T1-1 is a right H-module map and a left H-comodule map (similar to T2).On the other hand,for a unital algebra (no need to be associative),and a counital coassociative coalgebra A,if the coproduct and counit are both algebra morphisms,then the sufficient and necessary condition of A to be a Hopf quasigroup is that T1 is bijective,and T-11 is left compatible with ΔrT-11 and right compatible with m1T-11 at the same time (The properties are similar to T2).Furthermore,as a corollary,the quasigroups case is also considered.关键词
Galois线性映射/对极/Hopf代数/Hopf(余)拟群Key words
Galois linear map/antipode/Hopf algebra/Hopf (co) quasigroup分类
数理科学引用本文复制引用
谷乐,王伟,王栓宏..Galois线性映射及其构造[J].东南大学学报（英文版）,2019,35(4):522-526,5.基金项目
The National Natural Science Foundation of China (No.11371088,11571173,11871144),the Natural Science Foundation of Jiangsu Province (No.BK20171348). （No.11371088,11571173,11871144）
