Classification of finite-dimensional Hopf algebras over dual Radford algebras

Rongchuan Xiong; Naihong Hu

doi:10.36045/j.bbms.210612

Classification of finite-dimensional Hopf algebras over dual Radford algebras

Rongchuan Xiong
, Naihong Hu

School of Mathematical Sciences

School of Computer Science and Artificial Inteligent
Changzhou University

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We determine and classify all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero whose Hopf coradicals are isomorphic to dual Radford algebras of dimension 4p for a prime p > 5. In particular, we obtain families of new examples of finite-dimensional Hopf algebras without the dual Chevalley property.

Original language	English
Pages (from-to)	633-688
Number of pages	56
Journal	Bulletin of the Belgian Mathematical Society - Simon Stevin
Volume	28
Issue number	5
DOIs	https://doi.org/10.36045/j.bbms.210612
State	Published - Sep 2022

Keywords

Dual Chevalley property
Dual Radford algebra
Hopf algebra
Nichols algebra

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10.36045/j.bbms.210612

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title = "Classification of finite-dimensional Hopf algebras over dual Radford algebras",

abstract = "We determine and classify all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero whose Hopf coradicals are isomorphic to dual Radford algebras of dimension 4p for a prime p > 5. In particular, we obtain families of new examples of finite-dimensional Hopf algebras without the dual Chevalley property.",

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author = "Rongchuan Xiong and Naihong Hu",

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AU - Xiong, Rongchuan

AU - Hu, Naihong

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N2 - We determine and classify all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero whose Hopf coradicals are isomorphic to dual Radford algebras of dimension 4p for a prime p > 5. In particular, we obtain families of new examples of finite-dimensional Hopf algebras without the dual Chevalley property.

AB - We determine and classify all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero whose Hopf coradicals are isomorphic to dual Radford algebras of dimension 4p for a prime p > 5. In particular, we obtain families of new examples of finite-dimensional Hopf algebras without the dual Chevalley property.

KW - Dual Chevalley property

KW - Dual Radford algebra

KW - Hopf algebra

KW - Nichols algebra

UR - https://www.scopus.com/pages/publications/85145002238

U2 - 10.36045/j.bbms.210612

DO - 10.36045/j.bbms.210612

M3 - 文章

AN - SCOPUS:85145002238

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VL - 28

SP - 633

EP - 688

JO - Bulletin of the Belgian Mathematical Society - Simon Stevin

JF - Bulletin of the Belgian Mathematical Society - Simon Stevin

IS - 5

ER -

Classification of finite-dimensional Hopf algebras over dual Radford algebras

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