Finite dimensional Nichols algebras over $H_{c:{\sigma }_0}$ of Kashina

Abstract

Let $H$ be the Hopf algebra $H_{c:{\sigma }_0}$ of Kashina [J. Algebra, 232(2000),pp.617-663]. We give all simple Yetter-Drinfel'd modules $V$ over $H$, then classify all finite-dimensional Nichols algebras of $V$. The finite dimensional Nichols algebras of diagonal type are either $A_1,A_2$ or quantum planes, and non-diagonal type ones are $8$ or $16$ dimensional.