An Application of Finite Groups to Hopf algebras
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Published:2021-08-05
Issue:3
Volume:14
Page:816-828
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ISSN:1307-5543
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Container-title:European Journal of Pure and Applied Mathematics
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language:
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Short-container-title:Eur. J. Pure Appl. Math.
Author:
Al-Mutairi Tahani,
Al-shomrani Mohammed MosaORCID
Abstract
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.
Publisher
New York Business Global LLC
Subject
Applied Mathematics,Geometry and Topology,Numerical Analysis,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science