Eight classes of new Hopf algebras of dimension $128$ without the Chevalley property

Abstract

Classifying Hopf algebras of a given dimension is a hard and open question. Using the generalized lifting method, we determine all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero whose coradical generates a Hopf algebra $H$ of dimension $16$ without the Chevalley property and the corresponding infinitesimal braidings are simple objects in $\HYD$. In particular, we figure out $8$ classes of new Hopf algebras of dimension $128$ without the Chevalley property.

33 pages. arXiv admin note: substantial text overlap with arXiv:1612.04987

References in corpus (2)

• Liftings of Nichols algebras of diagonal type III. Cartan type $G_2$
• Some Hopf algebras of dimension $72$ without the Chevalley property

Cited by in corpus (2)

• Finite-dimensional Hopf algebras over the smallest non-pointed basic Hopf algebra
• On Hopf algebras over the unique $12$-dimensional Hopf algebra without the dual Chevalley property