Isomorphism classes of finite dimensional connected Hopf algebras in positive characteristic

Abstract

We classify all finite-dimensional connected Hopf algebras with large abelian primitive spaces. We show that they are Hopf algebra extensions of restricted enveloping algebras of certain restricted Lie algebras. For any abelian matched pair associated with these extensions, we construct a cohomology group, which classifies all the extensions up to equivalence. Moreover, we present a $1$-$1$ correspondence between the isomorphism classes and a group quotient of the cohomology group deleting some exceptional points, where the group respects the automorphisms of the abelian matched pair and the exceptional points represent those restricted Lie algebra extensions.

27 pages, any comment is welcome

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• Noetherian Hopf algebra domains of Gelfand-Kirillov dimension two
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Cited by in corpus (4)

• Classification of connected Hopf algebras of dimension $p^3$ I
• Finite symmetric integral tensor categories with the Chevalley property
• On non-connected pointed Hopf algebras of dimension 16 in characteristic 2
• Primitive Deformations of Quantum $p$-groups