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

^*此作品的通讯作者

数学科学学院

科研成果: 期刊稿件 › 文章 › 同行评审

3 引用（Scopus）

摘要

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.).

源语言	英语
页（从-至）	350-371
页数	22
期刊	Communications in Algebra
卷	51
期	1
DOI	https://doi.org/10.1080/00927872.2022.2099551
出版状态	已出版 - 2023

访问文件

10.1080/00927872.2022.2099551

其它文件与链接

链接到 Scopus 的出版物

引用此

@article{f653fa8f13304a64ae7f942164879f67,

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",

note = "Publisher Copyright: {\textcopyright} 2022 Taylor \& Francis Group, LLC.",

year = "2023",

doi = "10.1080/00927872.2022.2099551",

language = "英语",

volume = "51",

pages = "350--371",

journal = "Communications in Algebra",

issn = "0092-7872",

publisher = "Taylor and Francis Ltd.",

number = "1",

}

TY - JOUR

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

摘要

访问文件

其它文件与链接

指纹

引用此