Shuanhong Wang

Group Entwining Structures and Group Coalgebra Galois Extensions

Abstract The notions of group coalgebra Galois extension and group entwining structure are defined. It is proved that any group coalgebra Galois extension induces a unique group-entwining map ψ = {ψα, β}α, β∈π compatible with the right group coaction, generalizing the recent work of Brzeziński and Hajac [Brzeziński, T., Hajac, P. M. (1999). Coalgebra extensions and algebra coextensions of Galois type. Comm. Algebra 27:1347–1368].

Constructing New Braided T-Categories over Weak Hopf Algebras

Let AutweakHopf(H) denote the set of all automorphisms of a weak Hopf algebra H with bijective antipode in the sense of Böhm et al. (J Algebra 221:385–438, 1999) and let G be a certain crossed product group AutweakHopf(H)×AutweakHopf(H). The main purpose of this paper is to provide further examples of braided T-categories in the sense of Turaev (1994, 2008). For this, we first introduce a class of new categories

Quasitriangular Structures for a Class of Hopf Algebras of Dimension p 6

_{H}{\mathcal {WYD}}^{H}(\alpha, \beta)

Morita Contexts, π-Galois Extensions for Hopf π-Coalgebras

of weak (α, β)-Yetter-Drinfeld modules with α, β ∈ AutweakHopf(H) and we show that the category

The Duality Theorem for Weak Hopf Algebra (Co) Actions

{\mathcal WYD}(H) =\{{}_{H}\mathcal {WYD}^{H}(\alpha, \beta)\}_{(\alpha , \beta )\in G}

Bitwistor and Quasitriangular Structures of Bialgebras

becomes a braided T-category over G, generalizing the main constructions by Panaite and Staic (Isr J Math 158:349–365, 2007). Finally, when H is finite-dimensional we construct a quasitriangular weak T-coalgebra WD(H) = {WD(H)(α, β)}(α, β) ∈ G in the sense of Van Daele and Wang (Comm Algebra, 2008) over a family of weak smash product algebras

Constructing new braided T-categories over monoidal Hom-Hopf algebras

\{\overline{H^{*cop}\# H_{(\alpha,\beta)}}\}_{(\alpha , \beta)\in G}

General Double Quantum Groups

, and we obtain that

DOI-KOPPINEN HOPF BIMODULES ARE MODULES

{\mathcal {WYD}}(H)

New Turaev Braided Group Categories and Group Schur–Weyl Duality

is isomorphic to the representation category of the quasitriangular weak T-coalgebra WD(H).