A classification result on prime Hopf algebras of GK-dimension one

DOI10.1016/j.jalgebra.2019.12.003OpenAlexW2993406932MaRDI QIDQ2285246

Gongxiang Liu

Publication date: 16 January 2020

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

Full work available at URL: https://arxiv.org/abs/1804.08973

zbMATH Keywords

Hopf algebraprimeGK-dimension one

Mathematics Subject Classification ID

Group rings (16S34) Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) (16E65) Noetherian rings and modules (associative rings and algebras) (16P40) Hopf algebras and their applications (16T05)

Related Items (13)

Survey on Hopf algebras of GK-dimension 1 and 2 ⋮ The finite dual of commutative-by-finite Hopf algebras ⋮ Plane curves which are quantum homogeneous spaces ⋮ Affine commutative-by-finite Hopf algebras ⋮ Representations of a non-pointed Hopf algebra ⋮ A COMBINATORIAL IDENTITY AND THE FINITE DUAL OF INFINITE DIHEDRAL GROUP ALGEBRA ⋮ The Grothendieck rings of Wu–Liu–Ding algebras and their Casimir numbers (I) ⋮ Pointed Hopf algebras of discrete corepresentation type ⋮ Quotient Hopf algebras of the free bialgebra with PBW bases and GK-dimensions ⋮ The nodal cubic and quantum groups at roots of unity ⋮ Finite GK-dimensional pre-Nichols algebras of quantum linear spaces and of Cartan type ⋮ The structure of connected (graded) Hopf algebras ⋮ The Grothendieck rings of Wu-Liu-Ding algebras and their Casimir numbers (II)

Cites Work

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• Classification of affine prime regular Hopf algebras of GK-dimension one.
• Noetherian Hopf algebra domains of Gelfand-Kirillov dimension two.
• The structure of connected (graded) Hopf algebras
• The structure of Hopf algebras with a projection
• Classification of arithmetic root systems
• On the classification of finite-dimensional pointed Hopf algebras.
• Quantum groups and quantum shuffles
• Lifting of quantum linear spaces and pointed Hopf algebras of order \(p^3\)
• Spherical categories
• Cross products by braided groups and bosonization
• Hopf algebras of GK-dimension two with vanishing Ext-group
• The Weyl groupoid of a Nichols algebra of diagonal type
• Affine commutative-by-finite Hopf algebras
• Note on the Coradical Filtration ofD(m,d, ξ)
• Properties of pointed and connected Hopf algebras of finite Gelfand-Kirillov dimension
• Lower bounds of growth of Hopf algebras
• On Nichols algebras of diagonal type
• Prime regular Hopf algebras of GK-dimension one
• On Noetherian affine prime regular Hopf algebras of Gelfand-Kirillov dimension 1
• Liftings of Nichols Algebras of Diagonal Type I. Cartan Type A
• Noetherian PI Hopf algebras are Gorenstein
• A characterization of quantum groups
• Affine algebras of Gelfand-Kirillov dimension one are PI
• Connected (graded) Hopf algebras
• Connected Hopf algebras of Gelfand-Kirillov dimension four
• Tensor Categories
• Homological integral of Hopf algebras
• NOETHERIAN HOPF ALGEBRAS

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