Open AccessAn Application of Finite Groups to Hopf algebras
Author(s) -
Tahani Mazyad Almutairi,
M. M. Al-Shomrani
Publication year - 2021
Publication title -
european journal of pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.245
H-Index - 5
ISSN - 1307-5543
DOI - 10.29020/nybg.ejpam.v14i3.3979
Subject(s) - mathematics , hopf algebra , pure mathematics , algebraically closed field , algebra over a field , group (periodic table) , construct (python library) , field (mathematics) , discrete mathematics , chemistry , organic chemistry , computer science , programming language
Kaplansky’s famous conjectures about generalizing results from groups to Hopf al-gebras inspired many mathematicians to try to find solusions for them. Recently, Cohen and Westreich in [8] and [10] have generalized the concepts of nilpotency and solvability of groups to Hopf algebras under certain conditions and proved interesting results. In this article, we follow their work and give a detailed example by considering a finite group G and an algebraically closed field K. In more details, we construct the group Hopf algebra H = KG and examine its properties to see what of the properties of the original finite group can be carried out in the case of H.