Unifying Hopf modules

DOI10.1016/0021-8693(92)90160-NzbMath0782.16025MaRDI QIDQ1204455

Yukio Doi

Publication date: 10 March 1993

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

zbMATH Keywords

group-like elementsHopf algebrasHopf modulesequivalencesright comodule algebrasco-invariantscoalgebra mapsleft faithfully flat Galois extensionsright module coalgebras

Mathematics Subject Classification ID

Related Items (58)

Spin geometry on quantum groups via covariant differential calculi ⋮ A MONOIDAL STRUCTURE ON THE CATEGORY OF RELATIVE HOPF MODULES ⋮ Cibils–Rosso's Theorem for Quantum Groupoids ⋮ Group Entwining Structures and Group Coalgebra Galois Extensions ⋮ Relative projectivity and relative injectivity in the category of Doi-Hopf modules. II ⋮ FROBENIUS FUNCTORS OF THE SECOND KIND ⋮ Frobenius functors: applications ⋮ Integrals, quantum Galois extensions, and the affineness criterion for quantum Yetter-Drinfel'd modules ⋮ Morita equivalences induced by bimodules over Hopf-Galois extensions. ⋮ A Maschke type theorem for Doi-Hopf modules and applications ⋮ HOPF MODULES, MIYASHITA-ULBRICH COACTIONS, AND MONOIDAL CENTER CONSTRUCTIONS ⋮ Equivalence theorems and Hopf-Galois extensions ⋮ Crossed modules and Doi-Hopf modules ⋮ An algebraic framework for noncommutative bundles with homogeneous fibres ⋮ The coinduced functor for infinite dimensional Hopf algebras ⋮ Weak quasi-entwining structures ⋮ On the tensor product of bimodule categories over Hopf algebras. ⋮ Blattner–Cohen–Montgomery's Duality Theorem for (Weak) Group Smash Products ⋮ Comodule theories in Grothendieck categories and relative Hopf objects ⋮ Hopf modules, Frobenius functors and (one-sided) Hopf algebras ⋮ Crossed coproducts and cleft coextensions ⋮ Two-sided two-cosided Hopf modules and Doi-Hopf modules for quasi-Hopf algebras. ⋮ Injective envelopes, cogenerators and direct products in the Doi-Hopf module category. ⋮ Invertible bimodule categories over the representation category of a Hopf algebra ⋮ Group Corings and (Invertible) Weak Group Entwining Structures ⋮ Doi-Hopf modules, Yetter-Drinfel’d modules and Frobenius type properties ⋮ Picard groups of rings of coinvariants. ⋮ DOI-KOPPINEN HOPF BIMODULES ARE MODULES ⋮ Models of quasiprojective homogeneous spaces for Hopf algebras ⋮ On the cohomology of locally finite \(A\#_HC\)-modules. ⋮ Weak \(C\)-cleft extensions, weak entwining structures and weak Hopf algebras. ⋮ Duality theorems for crossed products over rings. ⋮ Double quantum groups ⋮ Weak \(C\)-cleft extensions and weak Galois extensions. ⋮ Entwined modules over linear categories and Galois extensions ⋮ Comodules and Corings ⋮ Hopf Algebras ⋮ Separable functors for the category of Doi Hom-Hopf modules ⋮ Braided monoidal categories and Doi–Hopf modules for monoidal Hom-Hopf algebras ⋮ Rational Modules for Corings ⋮ Galois and cleft monoidal cowreaths. Applications ⋮ GroupC-Rings and Weak Group Algebra Galois Coextensions ⋮ On the Cohomology of Relative Hopf Modules ⋮ Co-Frobenius Hopf algebras: Integrals, Doi-Koppinen modules and injective objects ⋮ The hopf modules category and the hopf equation ⋮ New types of bialgebras arising from the hopf equation ⋮ On modules associated to coalgebra Galois extensions ⋮ RELATIVE PROJECTIVITY AND RELATIVE INJECTIVITY IN THE CATEGORY OF DOI–HOPF MODULES ⋮ On generalized Hopf Galois extensions. ⋮ Hopf Semialgebras ⋮ Projectivity and freeness over comodule algebras ⋮ Doi-Koppinen modules for quantum groupoids. ⋮ Separable functors for the category of Doi-Hopf modules, applications ⋮ Hopf bimodules, coquasibialgebras, and an exact sequence of Kac ⋮ Separable functors in group coring. ⋮ Doi-hopf modules over weak hopf algebras ⋮ Triviality theorems for Yetter-Drinfel'd Hopf algebras. ⋮ Dual entwining structures and dual entwined modules.

Cites Work

• Unnamed Item
• Principal homogeneous spaces for arbitrary Hopf algebras
• Hopf-Galois extensions of algebras, the Miyashita-Ulbrich action, and Azumaya algebras
• Relative Hopf modules - equivalences and freeness criteria
• On Hopf algebras with cocommutative coradicals
• Modules graded by G-sets
• On the structure of relative hopf modules

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