Publications
Frobenius and separable functors for the category of entwined modules over cowreaths, I: General theory Vrije Universiteit Brussel
Entwined modules over cowreaths in a monoidal category are introduced. They can be identified to coalgebras in an appropriate monoidal category. It is investigated when such coalgebras are Frobenius (resp. separable), and when the forgetful functor from entwined modules to representations of the underlying algebra is Frobenius (resp. separable). These properties are equivalent when the unit object of the category is a ⊗-generator.
A Larson-Sweedler theorem for Hopf V-categories Vrije Universiteit Brussel
The aim of this paper is to extend the classical Larson-Sweedler theorem, namely that a k-bialgebra has a non-singular integral (and in particular is Frobenius) if and only if it is a finite dimensional Hopf algebra, to the ‘many-object’ setting of Hopf categories. To this end, we provide new characterizations of Frobenius V-categories and we develop the integral theory for Hopf V-categories. Our results apply to Hopf algebras in any braided ...
A note on the antipode for algebraic quantum groups Hasselt University KU Leuven
Behaviour of the Frobenius map in a non commutative world Vrije Universiteit Brussel
Some generalizations of preprojective algebras and their properties Hasselt University
Frobenius and separable functors for the category of entwined modules over cowreaths, II: Applications Vrije Universiteit Brussel
Let H be a quasi-Hopf algebra. We apply results obtained in [8] to give necessary and sufficient conditions for the forgetful functor from Doi–Hopf modules, two-sided Hopf modules or Yetter–Drinfeld modules over H to representations of the underlying algebra to be Frobenius (resp. separable). We show that in some situations these conditions reduce to the unimodularity and/or (co)semisimplicity of the quasi-Hopf algebra H.