Hopf group-coalgebras

DOI10.1016/S0022-4049(01)00125-6zbMath1011.16023arXivmath/0012073MaRDI QIDQ1612113

Alexis Virelizier

Publication date: 22 August 2002

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

Full work available at URL: https://arxiv.org/abs/math/0012073

zbMATH Keywords

antipodesintegralsgraded modulesgrouplike elementsHopf group-coalgebrasgroup-comodulesribbon Hopf coalgebras

Mathematics Subject Classification ID

Related Items (67)

Quasitriangular Hopf group-quasialgebras and generalized quantum Yang–Baxter equations ⋮ Group Twisted Smash Products and Doi–Hopf Modules forT-Coalgebras ⋮ Group Entwining Structures and Group Coalgebra Galois Extensions ⋮ Yetter-Drinfeld modules for crossed structures. ⋮ Double construction for crossed Hopf coalgebras. ⋮ The fundamental group of a Hopf linear category ⋮ A new approach to Rota–Baxter coalgebras ⋮ The Drinfel'd double for group-cograded multiplier Hopf algebras. ⋮ Hopf categories ⋮ The Morita contexts and galois extensions for weak Hopf group coalgebras ⋮ New Turaev braided group categories and weak (co)quasi-Turaev group coalgebras ⋮ On corepresentations of multiplier Hopf algebras. ⋮ Group-cograded multiplier Hopf (\(*\)-)algebras. ⋮ Rota-Baxter operators on Turaev's Hopf group (co)algebras. I: Basic definitions and related algebraic structures ⋮ The crossed structure of Hopf bimodules ⋮ Pivotal weak Turaev \(\pi \)-coalgebras ⋮ The structure theorem and duality theorem for endomorphism algebras of weak Hopf group coalgebras ⋮ Induced and coinduced representations of Hopf group coalgebras. ⋮ Group corings. ⋮ Modified symmetrized integral in G-coalgebras ⋮ New Braided Crossed Categories and Drinfel'd Quantum Double for Weak Hopf Group Coalgebras ⋮ Blattner–Cohen–Montgomery's Duality Theorem for (Weak) Group Smash Products ⋮ Algebras graded by discrete Doi-Hopf data and the Drinfeld double of a Hopf group-coalgebra. ⋮ Hopf \(\pi\)-crossed biproduct and related coquasitriangular structures. ⋮ Radford's biproducts for Hopf group-coalgebras and its quasitriangular structures. ⋮ Coquasitriangular Hopf group coalgebras and braided monoidal categories. ⋮ 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 ⋮ On the duality of generalized Lie and Hopf algebras. ⋮ The antipode of a quasitriangular quasi-Turaev group coalgebra is bijective ⋮ Group Corings and (Invertible) Weak Group Entwining Structures ⋮ A Maschke type theorem for weak group entwined modules and applications. ⋮ Modified graded Hennings invariants from unrolled quantum groups and modified integral ⋮ Graded Quantum Groups and Quasitriangular Hopf Group-Coalgebras ⋮ Gauge transformations for quasitriangular quasi-Turaev group coalgebras ⋮ New Turaev Braided Group Categories Over Entwining Structures ⋮ ON COREPRESENTATION OF HOPF π-COALGEBRAS ⋮ Two Results on Brzeziński π-crossed Product ⋮ Separable functors for the category of Doi-Hopf \(\pi\)-modules. ⋮ Quantum Double for a Weak T-Coalgebra ⋮ Ore extensions of quasitriangular Hopf group coalgebras ⋮ Constructing New Quasitriangular Turaev Group Coalgebras ⋮ Morita contexts and Galois theory for weak Hopf comodulelike algebras. ⋮ Constructing new braided \(T\)-categories over weak Hopf algebras. ⋮ Modified trace is a symmetrised integral ⋮ Rudiment of weak Doi-Hopf π-modules ⋮ A Class of Coquasitriangular Hopf Group Algebras ⋮ A Hennings type invariant of 3-manifolds from a topological Hopf superalgebra ⋮ Modified trace from pivotal Hopf \(G\)-coalgebras ⋮ Morita Contexts, π-Galois Extensions for Hopf π-Coalgebras ⋮ Quasitriangular Turaev Group Coalgebras and Radford's Biproduct ⋮ GroupC-Rings and Weak Group Algebra Galois Coextensions ⋮ Larson–Sweedler Theorem and Some Properties of Discrete Type in (G-Cograded) Multiplier Hopf Algebras ⋮ The quasitriangular structures for a class of group twisted product Hopf group coalgebras ⋮ On the Twisting and Drinfel'd Double for Multiplier Hopf Algebras ⋮ A Categorical Approach to Turaev's Hopf Group-Coalgebras ⋮ New braided \(T\)-categories over weak crossed Hopf group coalgebras ⋮ Traces on Multiplier Hopf Algebras ⋮ A class of braided monoidal categories via quasitriangular Hopf π-crossed coproduct algebras ⋮ Smash Products and π-H-Comodules of Linear Maps for HOPF π-Comodules ⋮ Quasitriangular Hopf group algebras and braided monoidal categories ⋮ Morita Contexts and Partial Group Galois Extensions for Hopf Group Coalgebras ⋮ A Class of Quasitriangular Hopf Group Coalgebras and Drinfel'd Double ⋮ New Turaev Braided Group Categories and Group Corings Based on Quasi-Hopf Group Coalgebras ⋮ Twisting Kuperberg invariants via Fox calculus and Reidemeister torsion ⋮ Separable functors in group coring. ⋮ TWISTED DRINFELD DOUBLES AND REPRESENTATIONS OF A HOPF ALGEBRA

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