New Braided Crossed Categories and Drinfel'd Quantum Double for Weak Hopf Group Coalgebras

DOI10.1080/00927870701509420zbMath1154.16031OpenAlexW2033134139MaRDI QIDQ3514770

Alfons Van Daele, Shuan-Hong Wang

Publication date: 23 July 2008

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

Full work available at URL: https://doi.org/10.1080/00927870701509420

zbMATH Keywords

weak Hopf algebrasYetter-Drinfeld modulesTuraev categoriesbraided crossed categoriesDrinfeld quantum doublesweak Hopf group-coalgebrasweak Hopf group-comodules

Mathematics Subject Classification ID

Related Items (16)

New Turaev braided group categories and weak (co)quasi-Turaev group coalgebras ⋮ A Maschke type theorem for weak relative Hopf \(\pi\)-modules. ⋮ Pivotal weak Turaev \(\pi \)-coalgebras ⋮ Algebras versus coalgebras ⋮ The Generalized C.M.Z.-Theorem and a Drinfel'd Double Construction for WT-Coalgebras and Graded Quantum Groupoids ⋮ Drinfel’d construction for Hom–Hopf T-coalgebras ⋮ The antipode of a quasitriangular quasi-Turaev group coalgebra is bijective ⋮ A Maschke type theorem for weak group entwined modules and applications. ⋮ Gauge transformations for quasitriangular quasi-Turaev group coalgebras ⋮ Morita contexts and Galois theory for weak Hopf comodulelike algebras. ⋮ Constructing new braided \(T\)-categories over weak Hopf algebras. ⋮ A Class of Coquasitriangular Hopf Group Algebras ⋮ New braided \(T\)-categories over weak crossed Hopf group coalgebras ⋮ A Generalized Drinfeld Quantum Double Construction Based on Weak Hopf Algebras ⋮ New Turaev Braided Group Categories and Group Corings Based on Quasi-Hopf Group Coalgebras ⋮ Yetter–Drinfel’d modules over weak Hopf quasigroups

Cites Work

• Unnamed Item
• Unnamed Item
• Frobenius and separable functors for generalized module categories and nonlinear equations
• Group-cograded multiplier Hopf (\(*\)-)algebras.
• An algebraic framework for group duality
• Braided tensor categories
• Hopf group-coalgebras
• Braided compact closed categories with applications to low dimensional topology
• Invariants of knots and 3-manifolds from quantum groupoids
• Yetter-Drinfeld modules for crossed structures.
• Double construction for crossed Hopf coalgebras.
• Weak Hopf algebras. I: Integral theory and \(C^*\)-structure
• Weak \(C\)-cleft extensions and weak Galois extensions.
• The Drinfel'd double for group-cograded multiplier Hopf algebras.
• Group Twisted Smash Products and Doi–Hopf Modules forT-Coalgebras
• Multiplier Hopf Algebras
• Doi-hopf modules over weak hopf algebras
• A Categorical Approach to Turaev's Hopf Group-Coalgebras

This page was built for publication: New Braided Crossed Categories and Drinfel'd Quantum Double for Weak Hopf Group Coalgebras