A freeness theorem for Nichols algebras

DOI10.1006/jabr.2000.8363zbMath0970.16017OpenAlexW2094101363MaRDI QIDQ1584612

Matías Graña

Publication date: 9 July 2001

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

Full work available at URL: https://doi.org/10.1006/jabr.2000.8363

zbMATH Keywords

braided Hopf algebraspointed Hopf algebrasNichols algebrasquantum symmetric algebrasrigid braided categoriesYetter-Drinfeld categories

Mathematics Subject Classification ID

Related Items (33)

The classification of Nichols algebras over groups with finite root system of rank two ⋮ Multinomial expansion and Nichols algebras associated to non-degenerate involutive solutions of the Yang-Baxter equation ⋮ Unnamed Item ⋮ Finite dimensional Hopf algebras over Kac-Paljutkin algebra $H_8$ ⋮ THE NICHOLS ALGEBRA OF SCREENINGS ⋮ On a factorization of graded Hopf algebras using Lyndon words. ⋮ Divisibility relations for the dimensions and Hilbert series of Nichols algebras of non-Abelian group type. ⋮ On Nichols algebras of infinite rank with finite Gelfand-Kirillov dimension ⋮ Fusion in the entwined category of Yetter-Drinfeld modules of a rank-1 Nichols algebra ⋮ On non-connected pointed Hopf algebras of dimension 16 in characteristic 2 ⋮ On the double of the (restricted) super Jordan plane ⋮ Constants of coordinate differential calculi defined by Yang-Baxter operators. ⋮ Rank 4 Nichols algebras of pale braidings ⋮ Pointed Hopf algebras of dimension \(p^2q\) in characteristic \(p\) ⋮ On Hopf algebras over basic Hopf algebras of dimension 24 ⋮ From racks to pointed Hopf algebras ⋮ Finite-dimensional pointed Hopf algebras over \(\mathbb S_4\). ⋮ On Nichols algebras over basic Hopf algebras ⋮ Finite-dimensional Hopf algebras over the Hopf algebra \(H_{d:-1,1}\) of Kashina ⋮ Finite-dimensional Hopf algebras over the Hopf algebra \(H_{b:1}\) of Kashina ⋮ PBW-bases of coideal subalgebras and a freeness theorem ⋮ Nichols algebras of group type with many quadratic relations. ⋮ Factorization of graded traces on Nichols algebras ⋮ On Hopf algebras over quantum subgroups ⋮ Duals of pointed Hopf algebras ⋮ On Hopf algebras over the unique 12-dimensional Hopf algebra without the dual Chevalley property ⋮ Cohomology rings of finite-dimensional pointed Hopf algebras over abelian groups ⋮ Finite-dimensional Nichols algebras over dual Radford algebras ⋮ Nonsemisimple Hopf algebras of dimension 8𝑝 with the Chevalley property ⋮ On Hopf algebras with triangular decomposition ⋮ Classification of finite-dimensional Hopf algebras over dual Radford algebras ⋮ On finite GK-dimensional Nichols algebras over abelian groups ⋮ Triviality theorems for Yetter-Drinfel'd Hopf algebras.

Cites Work

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• Finite Hopf algebras in braided tensor categories
• Quantum supergroups of \(\text{GL}(n| m)\) type: Differential forms, Koszul complexes, and Berezinians
• Finite quantum groups and Cartan matrices
• The ideals of free differential algebras
• Hopf algebras and vector symmetries
• A Hopf Algebra Freeness Theorem
• Pointed hopf algebras with large coradical

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