On non-connected pointed Hopf algebras of dimension 16 in characteristic 2

Abstract

Let $\mathbb{k}$ be an algebraically closed field. We give a complete classification of non-connected pointed Hopf algebras of dimension $16$ with char$\mathbb{k}=2$ that are generated by group-like elements and skew-primitive elements. It turns out that there are infinitely many classes (up to isomorphism) of pointed Hopf algebras of dimension 16. In particular, we obtain infinitely many new examples of non-commutative non-cocommutative finite-dimensional pointed Hopf algebras.

42 pages

References in corpus (11)

• Connected Hopf Algebras of Dimension $p^2$
• Classification of connected Hopf algebras of dimension $p^3$ I
• Classification of pointed rank one Hopf algebras
• Rank 2 Nichols Algebras of Diagonal Type over Fields of Positive Characteristic
• Classification of pointed Hopf algebras of dimension $p^2$ over any algebraically closed field
• Hopf algebras of prime dimension in positive characteristic
• Isomorphism classes of finite dimensional connected Hopf algebras in positive characteristic
• Pointed $p^3$-dimensional Hopf algebras in positive characteristic
• Modular quantizations of Lie algebras of Cartan type $H$ via Drinfeld Twists
• Examples of finite-dimensional pointed Hopf algebras in characteristic $2$
• Modular Quantizations of Lie Algebras of Cartan Type K via Drinfeld Twists of Jordanian Type

Cited by in corpus (1)

• Pointed Hopf algebras of dimension $p^{2}q$ in characteristic $p$