On some classification of finite-dimensional Hopf algebras over the Hopf algebra of Kashina

Yiwei Zheng; Yun Gao; Naihong Hu; Yuxing Shi

doi:10.1080/00927872.2022.2099551

On some classification of finite-dimensional Hopf algebras over the Hopf algebra of Kashina

Yiwei Zheng^*
, Yun Gao
, Naihong Hu
, Yuxing Shi

^*Corresponding author for this work

School of Mathematical Sciences

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

3 Scopus citations

Abstract

Let H be the dual of 16-dimensional nontrivial semisimple Hopf algebra (Formula presented.) in the classification work of Kashina [22]. We completely determine all finite-dimensional Nichols algebras satisfying (Formula presented.) where (Formula presented.) each N_i is a simple object in (Formula presented.) Under this assumption, we classify all those Hopf algebras of finite-dimensional growth from the semisimple Hopf algebra H via the relevant Nichols algebras (Formula presented.).

Original language	English
Pages (from-to)	350-371
Number of pages	22
Journal	Communications in Algebra
Volume	51
Issue number	1
DOIs	https://doi.org/10.1080/00927872.2022.2099551
State	Published - 2023

Keywords

Classification
Nichols algebra
Yetter-Drinfeld module
semisimple Hopf algebra

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10.1080/00927872.2022.2099551

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title = "On some classification of finite-dimensional Hopf algebras over the Hopf algebra of Kashina",

abstract = "Let H be the dual of 16-dimensional nontrivial semisimple Hopf algebra (Formula presented.) in the classification work of Kashina [22]. We completely determine all finite-dimensional Nichols algebras satisfying (Formula presented.) where (Formula presented.) each Ni is a simple object in (Formula presented.) Under this assumption, we classify all those Hopf algebras of finite-dimensional growth from the semisimple Hopf algebra H via the relevant Nichols algebras (Formula presented.).",

keywords = "Classification, Nichols algebra, Yetter-Drinfeld module, semisimple Hopf algebra",

author = "Yiwei Zheng and Yun Gao and Naihong Hu and Yuxing Shi",

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year = "2023",

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T1 - On some classification of finite-dimensional Hopf algebras over the Hopf algebra of Kashina

AU - Zheng, Yiwei

AU - Gao, Yun

AU - Hu, Naihong

AU - Shi, Yuxing

PY - 2023

Y1 - 2023

N2 - Let H be the dual of 16-dimensional nontrivial semisimple Hopf algebra (Formula presented.) in the classification work of Kashina [22]. We completely determine all finite-dimensional Nichols algebras satisfying (Formula presented.) where (Formula presented.) each Ni is a simple object in (Formula presented.) Under this assumption, we classify all those Hopf algebras of finite-dimensional growth from the semisimple Hopf algebra H via the relevant Nichols algebras (Formula presented.).

AB - Let H be the dual of 16-dimensional nontrivial semisimple Hopf algebra (Formula presented.) in the classification work of Kashina [22]. We completely determine all finite-dimensional Nichols algebras satisfying (Formula presented.) where (Formula presented.) each Ni is a simple object in (Formula presented.) Under this assumption, we classify all those Hopf algebras of finite-dimensional growth from the semisimple Hopf algebra H via the relevant Nichols algebras (Formula presented.).

KW - Classification

KW - Nichols algebra

KW - Yetter-Drinfeld module

KW - semisimple Hopf algebra

UR - https://www.scopus.com/pages/publications/85134592083

U2 - 10.1080/00927872.2022.2099551

DO - 10.1080/00927872.2022.2099551

M3 - 文章

AN - SCOPUS:85134592083

SN - 0092-7872

VL - 51

SP - 350

EP - 371

JO - Communications in Algebra

JF - Communications in Algebra

IS - 1

ER -

On some classification of finite-dimensional Hopf algebras over the Hopf algebra of Kashina

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Keywords

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