Picard-Vessiot extensions of Artinian simple module algebras.

DOI10.1016/j.jalgebra.2004.12.006zbMath1107.16037OpenAlexW1991737576MaRDI QIDQ1772447

Akira Masuoka, Katsutoshi Amano

Publication date: 18 April 2005

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2004.12.006

zbMATH Keywords

difference fieldsdifferential fieldsPicard-Vessiot extensionsArtinian simple module algebraspointed smooth Hopf algebras

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Differential algebra (12H05) Difference algebra (12H10) Hopf algebras and their applications (16T05)

Related Items (21)

Twisted forms of differential Lie algebras over \(\mathbb{C}(t)\) associated with complex simple Lie algebras ⋮ ×_R-BIALGEBRAS ASSOCIATED WITH ITERATIVE q-DIFFERENCE RINGS ⋮ Existence of \(\partial\)-parameterized Picard-Vessiot extensions over fields with algebraically closed constants ⋮ Difference Galois theory of linear differential equations ⋮ Stratified order one differential equations in positive characteristic ⋮ LARGE FIELDS IN DIFFERENTIAL GALOIS THEORY ⋮ A Chevalley theorem for difference equations ⋮ Galois theory for iterative connections and nonreduced Galois groups ⋮ Hopf Algebraic Approach to Picard-Vessiot Theory ⋮ Differential embedding problems over Laurent series fields ⋮ A difference version of Nori's theorem ⋮ Differential Galois groups over Laurent series fields ⋮ Generalized \(q\)-boson algebras and their integrable modules ⋮ Picard-Vessiot extensions of real differential fields ⋮ Generalized differentials and prolongation spaces ⋮ Liouville Extensions of Artinian Simple Module Algebras ⋮ The \(kS_3\)-module algebra structures on \(M_3(k)\) ⋮ Generalized linear cellular automata in groups and difference Galois theory ⋮ A categorical approach to Picard-Vessiot theory ⋮ Non-free iterative differential modules ⋮ Galois Theory of Difference Equations with Periodic Parameters

Cites Work

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• Biinvertible actions of Hopf algebras
• Differential Galois theory and tensor products
• A Hopf algebraic approach to the Picard-Vessiot theory
• Relative Hopf modules - equivalences and freeness criteria
• Galois theory of difference equations
• Hopf module duality applied to X-outer Galois theory.
• The Lasker-Noether theorem for commutative and Noetherian module algebras over a pointed Hopf algebra.
• A correspondence between Hopf ideals and sub-Hopf algebras
• The Predual Theorem to the Jacobson-Bourbaki Theorem
• Différentielles non commutatives et théorie de Galois différentielle ou aux différences

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