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6 papers · 1 filter
Involutive Yang-Baxter Groups
Ferran Cedo, Eric Jespers, Angel del Rio
In 1992 Drinfeld posed the question of finding the set theoretic solutions of the Yang-Baxter equation. Recently, Gateva-Ivanova and Van den Bergh and Etingof, Schedler and Solovie…
A categorical approach to Turaev's Hopf group-coalgebras
S. Caenepeel, M. De Lombaerde
We show that Turaev's group-coalgebras and Hopf group-coalgebras are coalgebras and Hopf algebras in a symmetric monoidal category, which we call the Turaev category. A similar res…
Doi-Hopf modules and Yetter-Drinfeld modules for quasi-Hopf algebras
D. Bulacu, S. Caenepeel, B. Torrecillas
For a quasi-Hopf algebra , a left -comodule algebra $\mf{B}$ and a right -module coalgebra we will characterize the category of Doi-Hopf modules ${}^C{\cal M}(H)_{\mf{…
Yetter-Drinfeld categories for quasi-Hopf algebras
D. Bulacu, S. Caenepeel, F. Panaite
We show that all possible categories of Yetter-Drinfeld modules over a quasi-Hopf algebra are isomorphic. We prove also that the category $\yd^{\rm fd}$ of finite dimensional l…
Two-sided (two-cosided) Hopf modules and Doi-Hopf modules for quasi-Hopf algebras
D. Bulacu, S. Caenepeel
Let be a finite dimensional quasi-Hopf algebra over a field and a right -comodule algebra in the sense of Hausser and Nill. We first show that on the …
Semisimplicity of the categories of Yetter-Drinfeld modules and Long dimodules
S. Caenepeel, T. Guédénon
Let be a field, and a Hopf algebra with bijective antipode. If is commutative, noetherian, semisimple and cosemisimple, then the category of Y…