Examples of finite-dimensional pointed Hopf algebras in positive characteristic

Abstract

We present new examples of finite-dimensional Nichols algebras over fields of positive characteristic. The corresponding braided vector spaces are not of diagonal type, admit a realization as Yetter-Drinfeld modules over finite abelian groups and are analogous to braidings over fields of characteristic zero whose Nichols algebras have finite Gelfand-Kirillov dimension described in arXiv:1606.02521. We obtain nex examples of finite-dimensional pointed Hopf algebras by bosonization with group algebras of suitable finite abelian groups.

30 pages. arXiv admin note: text overlap with arXiv:1606.02521. v2: minor changes. To appear in Progr. Math., a volume in honor of Prof. Reshetikhin