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

被引：7
|
作者：
Zheng, Yiwei [1 ]
Gao, Yun [2 ]
Hu, Naihong [3 ]
机构：
[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
[2] York Univ, Dept Math & Stat, Toronto, ON M3J 1P3, Canada
[3] East China Normal Univ, Sch Math Sci, Shanghai Key Lab PMMP, Shanghai 200241, Peoples R China
来源：
JOURNAL OF ALGEBRA | 2021年 / 567卷
基金：
加拿大自然科学与工程研究理事会;
关键词：
Semisimple Hopf algebra; Nichols algebra; Yetter-Drinfeld module; Classification; NICHOLS ALGEBRAS; CLASSIFICATION;
D O I：
10.1016/j.jalgebra.2020.09.035
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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) similar or equal to circle times(i is an element of I) B(V-i), where V = circle plus(i is an element of I) V-i, each V-i is a simple object in (H)(H) yD. Finally, we describe all liftings of those B(V) over H. (C) 2020 Elsevier Inc. All rights reserved.
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页码：613 / 659
页数：47
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