|Table of Contents|

[1] Gu Yue, Wang Wei, Wang Shuanhong,. Galois linear maps and their construction [J]. Journal of Southeast University (English Edition), 2019, 35 (4): 522-526. [doi:10.3969/j.issn.1003-7985.2019.04.016]

Galois linear maps and their construction()

Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

2019 4
Research Field:
Mathematics, Physics, Mechanics
Publishing date:


Galois linear maps and their construction
Gu Yue1 Wang Wei2 Wang Shuanhong1
1School of Mathematics, Southeast University, Nanjing 211189, China
2Nanjing Research Institute of Electronic Engineering, Nanjing 210007, China
Galois linear map antipode Hopf algebra Hopf(co)quasigroup
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 Galois 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, T-11 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 ΔrrT-11 and right compatible with mlT-11 at the same time(The properties are similar to T2). Furthermore, as a corollary, the quasigroups case is also considered.


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Biographies: Gu Yue(1992—), female, graduate; Wang Shuanhong(corresponding author), male, doctor, professor, shuanhwang@seu.edu.cn.
Foundation items: The National Natural Science Foundation of China(No.11371088, 11571173, 11871144), the Natural Science Foundation of Jiangsu Province(No.BK20171348).
Citation: Gu Yue, Wang Wei, Wang Shuanhong. Galois linear maps and their construction[J].Journal of Southeast University(English Edition), 2019, 35(4):522-526.DOI:10.3969/j.issn.1003-7985.2019.04.016.
Last Update: 2019-12-20