On some classification of finite-dimensional Hopf algebras over the Hopf algebra Hb:1* of Kashina

作者：Zheng, Yiwei^*; Gao, Yun; Hu, Naihong; Shi, Yuxing

来源：Communications in Algebra, 2023, 51(1): 350-371.

DOI：10.1080/00927872.2022.2099551

• Classification
• Nichols algebra
• semisimple Hopf algebra
• Yetter-Drinfeld module

Let H be the dual of 16-dimensional nontrivial semisimple Hopf algebra H-b:1 in the classification work of Kashina [22]. We completely determine all finite-dimensional Nichols algebras satisfying B(N) similar or equal to circle times(i is an element of l) B(N-i), where N = circle plus(i is an element of l) N-i, each N-i is a simple object in (HYD)-Y-H. Under this assumption, we classify all those Hopf algebras of finite-dimensional growth from the semi-simple Hopf algebra H via the relevant Nichols algebras B(N).

• 单位
  杭州师范大学