On Noetherian affine prime regular Hopf algebras of Gelfand-Kirillov dimension 1

DOI10.1090/S0002-9939-08-09034-5zbMath1175.16025OpenAlexW2019959507MaRDI QIDQ3617563

Gongxiang Liu

Publication date: 30 March 2009

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-08-09034-5

zbMATH Keywords

Gelfand-Kirillov dimensionTaft algebrashomological integrals

Mathematics Subject Classification ID

Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) (16E65) Growth rate, Gelfand-Kirillov dimension (16P90) Hopf algebras and their applications (16T05)

Related Items

Classification of affine prime regular Hopf algebras of GK-dimension one. ⋮ Survey on Hopf algebras of GK-dimension 1 and 2 ⋮ Homological integral of Hopf algebras ⋮ Finite GK-dimensional pre-Nichols algebras of super and standard type ⋮ Finite GK-dimensional pre-Nichols algebras of (super)modular and unidentified type ⋮ Hopf algebras of GK-dimension two with vanishing Ext-group ⋮ Existence of Hopf subalgebras of GK-dimension two. ⋮ NOETHERIAN HOPF ALGEBRAS ⋮ A classification result on prime Hopf algebras of GK-dimension one ⋮ The structure of connected (graded) Hopf algebras ⋮ Connected Hopf algebras of Gelfand-Kirillov dimension four ⋮ On finite GK-dimensional Nichols algebras over abelian groups

Cites Work

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• An operator-theoretic approach to invariant integrals on quantum homogeneous \(\text{SU}_{n,1}\)-spaces
• On the structure of tame graded basic Hopf algebras.
• On Crossed Products of Hopf Algebras
• Noetherian PI Hopf algebras are Gorenstein
• Affine algebras of Gelfand-Kirillov dimension one are PI
• Homological integral of Hopf algebras

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