Finite-dimensional Hopf algebras of rank one in characteristic zero

By L. Krop, D. Radford. 2006

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Let H be a finite-dimensional pointed Hopf algebra over an algebraically closed field k generated as an algebra by the first term H1 of its coradical filtration. Generally for a Hopf algebra whose coradical H0 is a sub-Hopf algebra we assign a measure of complexity to H which we refer to as the rank of H. We obtain a presentation of pointed Hopf algebras H of rank one by generators and relations. In the special case when G(H) is an abelian group and k has characteristic 0 we classify the finite-dimensional indecomposable H-modules, determine all simple left modules of the Drinfel'd double D(H) of H, their projective covers, and the blocks of D(H).

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f93d61e4a2e756e27a5ea18ad138860e7eb368d1