Finite-dimensional Hopf algebras of rank one in characteristic zero.

DOI10.1016/j.jalgebra.2006.03.031zbMath1126.16028OpenAlexW1990633609MaRDI QIDQ852673

Leonid Krop, David E. Radford

Publication date: 15 November 2006

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2006.03.031

zbMATH Keywords

representationsranksDrinfeld doublescoradical filtrationsfinite dimensional pointed Hopf algebrastuple data

Mathematics Subject Classification ID

Related Items (28)

Indecomposable decomposition of tensor products of modules over Drinfeld doubles of Taft algebras ⋮ Pointed Hopf actions on fields. II ⋮ Tensor product decomposition rules for weight modules over the Hopf–Ore extensions of group algebras ⋮ Actions of quantum linear spaces on quantum algebras ⋮ Representations of Hopf-Ore extensions of group algebras ⋮ A class of quantum doubles of pointed Hopf algebras of rank one ⋮ On Hopf algebras over basic Hopf algebras of dimension 24 ⋮ Green rings of pointed rank one Hopf algebras of non-nilpotent type. ⋮ Classification of pointed Hopf algebras of dimension \(p^2\) over any algebraically closed field. ⋮ Classification of pointed rank one Hopf algebras. ⋮ The corepresentation ring of a pointed Hopf algebra of rank one ⋮ Trace-Like Invariant for Representations of Nilpotent Liftings of Quantum Planes ⋮ The cohomology of monogenic extensions in the noncommutative setting. ⋮ Idempotents of the Green algebras of finite dimensionalpointed rank one Hopf algebras of nilpotent type ⋮ Green rings of pointed rank one Hopf algebras of nilpotent type. ⋮ A class of Drinfeld doubles that are ribbon algebras. ⋮ Factorization of simple modules for certain pointed Hopf algebras. ⋮ Tensor Products of Modules Over a Certain Class of Quantum Doubles ⋮ Hopf algebras which factorize through the Taft algebra \(T_{m^{2}}(q)\) and the group Hopf algebra \(K[C_{n}\)] ⋮ Primitive cohomology of Hopf algebras ⋮ Cyclic homology of monogenic extensions in the noncommutative setting. ⋮ Bialgebra cohomology, pointed Hopf algebras, and deformations. ⋮ REPRESENTATION THEORY OF LIFTINGS OF QUANTUM PLANES ⋮ Cleft extensions of a family of braided Hopf algebras ⋮ Representations of pointed Hopf algebras and their Drinfel'd quantum doubles. ⋮ Green ring of the category of weight modules over the Hopf–Ore extensions of group algebras ⋮ Hopf quivers and Nichols algebras in positive characteristic ⋮ Representations of Hopf-Ore extensions of group algebras and pointed Hopf algebras of rank one.

Cites Work

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• Biinvertible actions of Hopf algebras
• Finite-dimensional simple-pointed Hopf algebras
• On antipodes in pointed Hopf algebras
• Minimal quasitriangular Hopf algebras
• Modular representations of classical Lie algebras and semi-simple groups
• Über Untergruppen endlicher algebraischer Gruppen
• IRREDUCIBLE REPRESENTATIONS OF LIFTINGS OF QUANTUM PLANES
• On a coradical of a finite-dimensional Hopf algebra

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