Finite-dimensional Hopf algebras over the Hopf algebra Hb:1 of Kashina

Yiwei Zheng; Yun Gao; Naihong Hu

doi:10.1016/j.jalgebra.2020.09.035

Finite-dimensional Hopf algebras over the Hopf algebra H_b:1 of Kashina

Yiwei Zheng, Yun Gao, Naihong Hu^*

^*Corresponding author for this work

School of Mathematical Sciences

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

7 Scopus citations

Abstract

Let H be the 16-dimensional nontrivial semisimple Hopf algebra H_b:1 appeared in Kashina's work [32]. We obtain all simple Yetter-Drinfeld modules over H and then determine all finite-dimensional Nichols algebras satisfying B(V)≅⨂_i∈IB(V_i), where V=⨁_i∈IV_i, each V_i is a simple object in YDHH. Finally, we describe all liftings of those B(V) over H.

Original language	English
Pages (from-to)	613-659
Number of pages	47
Journal	Journal of Algebra
Volume	567
DOIs	https://doi.org/10.1016/j.jalgebra.2020.09.035
State	Published - 1 Feb 2021

Keywords

Classification
Nichols algebra
Semisimple Hopf algebra
Yetter-Drinfeld module

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10.1016/j.jalgebra.2020.09.035

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title = "Finite-dimensional Hopf algebras over the Hopf algebra Hb:1 of Kashina",

abstract = "Let H be the 16-dimensional nontrivial semisimple Hopf algebra Hb:1 appeared in Kashina's work [32]. We obtain all simple Yetter-Drinfeld modules over H and then determine all finite-dimensional Nichols algebras satisfying B(V)≅⨂i∈IB(Vi), where V=⨁i∈IVi, each Vi is a simple object in YDHH. Finally, we describe all liftings of those B(V) over H.",

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

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

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doi = "10.1016/j.jalgebra.2020.09.035",

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T1 - Finite-dimensional Hopf algebras over the Hopf algebra Hb:1 of Kashina

AU - Zheng, Yiwei

AU - Gao, Yun

AU - Hu, Naihong

PY - 2021/2/1

Y1 - 2021/2/1

N2 - Let H be the 16-dimensional nontrivial semisimple Hopf algebra Hb:1 appeared in Kashina's work [32]. We obtain all simple Yetter-Drinfeld modules over H and then determine all finite-dimensional Nichols algebras satisfying B(V)≅⨂i∈IB(Vi), where V=⨁i∈IVi, each Vi is a simple object in YDHH. Finally, we describe all liftings of those B(V) over H.

AB - Let H be the 16-dimensional nontrivial semisimple Hopf algebra Hb:1 appeared in Kashina's work [32]. We obtain all simple Yetter-Drinfeld modules over H and then determine all finite-dimensional Nichols algebras satisfying B(V)≅⨂i∈IB(Vi), where V=⨁i∈IVi, each Vi is a simple object in YDHH. Finally, we describe all liftings of those B(V) over H.

KW - Classification

KW - Nichols algebra

KW - Semisimple Hopf algebra

KW - Yetter-Drinfeld module

UR - https://www.scopus.com/pages/publications/85092692716

U2 - 10.1016/j.jalgebra.2020.09.035

DO - 10.1016/j.jalgebra.2020.09.035

M3 - 文章

AN - SCOPUS:85092692716

SN - 0021-8693

VL - 567

SP - 613

EP - 659

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Finite-dimensional Hopf algebras over the Hopf algebra H_b:1 of Kashina

Abstract

Keywords

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