The Noether problem for Hopf algebras

DOI10.4171/JNCG/237zbMath1372.16039arXiv1404.4941MaRDI QIDQ740096

Akira Masuoka, Christian Kassel

Publication date: 12 August 2016

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.4941

zbMATH Keywords

Hopf algebrainvariant theorylocalizationrationalitypolynomial identitiesNoether problem

Mathematics Subject Classification ID

Group rings (16S34) Actions of groups on commutative rings; invariant theory (13A50) Transcendental field extensions (12F20) Rings of fractions and localization for commutative rings (13B30) Hopf algebras and their applications (16T05) Coalgebras and comodules; corings (16T15)

Cites Work

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• Examples of polynomial identities distinguishing the Galois objects over finite-dimensional Hopf algebras.
• Noether's problem over an algebraically closed field
• The structure of Hopf algebras with a projection
• Polynomial identities and noncommutative versal torsors.
• Relative Hopf modules - equivalences and freeness criteria
• On Hopf algebras with cocommutative coradicals
• Invariant rational functions and a problem of Steenrod
• Free Hopf algebras generated by coalgebras
• Generic Hopf Galois extensions
• Flatness and freeness properties of the generic Hopf Galois extensions
• Generic base algebras and universal comodule algebras for some finite-dimensional Hopf algebras
• Graded identities of matrix algebras and the universal graded algebra

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