Variations on the smash product with applications to group-graded rings

DOI10.1016/0022-4049(94)00124-2zbMath0838.16035OpenAlexW2113615439MaRDI QIDQ1903698

M. Koppinen

Publication date: 29 May 1996

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(94)00124-2

zbMATH Keywords

crossed productsHopf algebrasbialgebrasHopf modulesduality theoremssmash product algebrasright \(H\)-comodule algebrasgeneralized smash products\(G\)-graded rings\(H\)-module coalgebras

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Graded rings and modules (associative rings and algebras) (16W50) Twisted and skew group rings, crossed products (16S35) Smash products of general Hopf actions (16S40)

Related Items (27)

Cibils–Rosso's Theorem for Quantum Groupoids ⋮ FROBENIUS FUNCTORS OF THE SECOND KIND ⋮ Integrals, quantum Galois extensions, and the affineness criterion for quantum Yetter-Drinfel'd modules ⋮ Duality theorems for graded algebras and coalgebras ⋮ Descent and Galois theory for Hopf categories ⋮ An algebraic framework for noncommutative bundles with homogeneous fibres ⋮ Weak quasi-entwining structures ⋮ Coideal subalgebras in hopf algebras: freeness, integrals, smash products ⋮ Two-sided two-cosided Hopf modules and Doi-Hopf modules for quasi-Hopf algebras. ⋮ Weak \(C\)-cleft extensions, weak entwining structures and weak Hopf algebras. ⋮ Duality theorems for crossed products over rings. ⋮ Weak \(C\)-cleft extensions and weak Galois extensions. ⋮ Comodules and Corings ⋮ Rational Modules for Corings ⋮ Galois and cleft monoidal cowreaths. Applications ⋮ Co-Frobenius Hopf algebras: Integrals, Doi-Koppinen modules and injective objects ⋮ Doi–Hopf Modules and Yetter–Drinfeld Modules for Quasi-Hopf Algebras ⋮ The hopf modules category and the hopf equation ⋮ On modules associated to coalgebra Galois extensions ⋮ On generalized Hopf Galois extensions. ⋮ Hopf Semialgebras ⋮ Comodules graded by g–sets and applications ⋮ Doi-Koppinen modules for quantum groupoids. ⋮ Separable functors for the category of Doi-Hopf modules, applications ⋮ Morphisms of relative Hopf modules, smash products, and duality ⋮ Doi-hopf modules over weak hopf algebras ⋮ Dual entwining structures and dual entwined modules.

Cites Work

• A duality theorem for Hopf module algebras
• Crossed products and Galois extensions of Hopf algebras
• Infinite group-graded rings, rings of endomorphisms, and localization
• Ext//ad(SpR,\(mu^ A)\)=Br(A/k)
• Relative Hopf modules - equivalences and freeness criteria
• A duality theorem for crossed products of Hopf algebras
• A correspondence between Hopf ideals and sub-Hopf algebras
• Modules with decompositions that complement direct summands
• Modules graded by G-sets
• Cleft cqmodule algebras and hopf modules
• Crossed Products and Inner Actions of Hopf Algebras
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