Non-semisimple Hopf algebras of dimension \(p^2\).

DOI10.1016/S0021-8693(02)00139-4zbMath1041.16028arXivmath/0110223OpenAlexW1993828024MaRDI QIDQ1858185

Siu-Hung Ng

Publication date: 12 February 2003

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

Full work available at URL: https://arxiv.org/abs/math/0110223

zbMATH Keywords

group-like elementsHopf algebrasantipodesintegralsTaft algebras

Mathematics Subject Classification ID

Related Items

On Hopf algebras of dimension \(pq\). ⋮ Hopf algebras of dimension \(pq\). ⋮ HOPF ALGEBRAS OF DIMENSION 30 ⋮ Almost involutive Hopf-Ore extensions of low dimension ⋮ Non-simple quasitriangular Hopf algebras of dimension \(pq^2\) ⋮ STRUCTURE OF CORADICAL FILTRATION AND ITS APPLICATION TO HOPF ALGEBRAS OF DIMENSIONpq ⋮ Actions of Taft's algebras on finite dimensional algebras ⋮ Lie structure on Hopf algebra cohomology ⋮ On finite-dimensional semisimple Hopf algebras of dimension \(n(n+1)\). ⋮ Classification of pointed Hopf algebras of dimension \(p^2\) over any algebraically closed field. ⋮ Hopf algebras of dimension \(pq\). II. ⋮ Generic Modules Over a Class of Drinfeld's Quantum Doubles ⋮ REPRESENTATIONS OF A CLASS OF DRINFELD'S DOUBLES ⋮ On Hopf algebras of dimension \(4p\). ⋮ Hopf algebras of dimension $2p$ ⋮ Degeneration, Rigidity and Irreducible Components of Hopf algebras ⋮ Classification of Semisimple Hopf Algebras ⋮ Hopf algebras of dimension 16. ⋮ Classification of Hopf algebras of dimension 18. ⋮ Techniques for Classifying Hopf Algebras and Applications to Dimensionp³ ⋮ A survey of Hopf algebras of low dimension.

Cites Work

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• A necessary and sufficient condition for a finite-dimensional Drinfel'd double to be a ribbon Hopf algebra
• Biinvertible actions of Hopf algebras
• The structure of Hopf algebras with a projection
• Finite dimensional cosemisimple Hopf algebras in characteristic 0 are semisimple
• Crossed products and Galois extensions of Hopf algebras
• Normal basis and transitivity of crossed products for Hopf algebras
• Semisimple Hopf algebras of dimension \(pq\) are trivial
• The trace function and Hopf algebras
• Semisimple Hopf algebras
• Hopf algebras of order \(p^2\) and braided Hopf algebras of order \(p\)
• The Group of Automorphisms of a Semisimple Hopf Algebra Over a Field of Characteristic 0 is Finite
• Semisimple Cosemisimple Hopf Algebras
• A Hopf Algebra Freeness Theorem
• The Order of the Antipode of a Finite Dimensional Hopf Algebra is Finite
• The $p^n$ theorem for semisimple Hopf algebras
• The Order of the Antipode of Finite-dimensional Hopf Algebra

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