Pointed Hopf algebras and Kaplansky's 10th conjecture

DOI10.1006/jabr.1998.7513zbMath0922.16023arXivmath/9801130OpenAlexW2010039028WikidataQ122876102 ScholiaQ122876102MaRDI QIDQ1277016

Shlomo Gelaki

Publication date: 18 October 1999

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9801130

zbMATH Keywords

group algebrasgroup-like elementsskew-primitive elementsself-dualitieslinear basesright integralsminimal quasitriangular Hopf algebraspointed finite-dimensional Hopf algebrasunimodular Hopf algebras

Mathematics Subject Classification ID

Related Items

Unnamed Item ⋮ Pointed Hopf algebras with triangular decomposition. A characterization of multiparameter quantum groups ⋮ Finite quantum groups over abelian groups of prime exponent ⋮ REPRESENTATIONS OF SIMPLE POINTED HOPF ALGEBRAS ⋮ Every central simple algebra is Brauer equivalent to a Hopf Schur algebra. ⋮ Introduction to the Yang-Baxter equation with open problems. ⋮ Almost-triangular Hopf algebras. ⋮ Constructing pointed Hopf algebras by Ore extensions ⋮ Defending the negated Kaplansky conjecture ⋮ Some Hopf algebras related to sl2 ⋮ On Hopf algebras of dimension \(4p\). ⋮ Quasitriangular Structures for a Class of Hopf Algebras of Dimensionp⁶ ⋮ Degeneration, Rigidity and Irreducible Components of Hopf algebras ⋮ Classification of Semisimple Hopf Algebras ⋮ Hopf Algebras ⋮ An isomorphism theorem for ore extension hopf algebras ⋮ Duals of pointed Hopf algebras ⋮ Lifting of quantum linear spaces and pointed Hopf algebras of order \(p^3\) ⋮ Nonsemisimple Hopf algebras of dimension 8𝑝 with the Chevalley property ⋮ A survey of Hopf algebras of low dimension. ⋮ Pointed hopf algebras of dimension 32 ⋮ Finite quantum groups and Cartan matrices ⋮ Lifting of Nichols algebras of type \(B_2\). (With an appendix ``A generalization of the \(q\)-binomial theorem with I. Rutherford).

Cites Work

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• Addendum: On pointed ribbon Hopf algebras
• On antipodes in pointed Hopf algebras
• On pointed ribbon Hopf algebras
• Minimal quasitriangular Hopf algebras
• The Coradical Filtration for Quantized Enveloping Algebras
• The Order of the Antipode of Finite-dimensional Hopf Algebra