Half-liberated real spheres and their subspaces

We describe the quantum subspaces of Banica-Goswami's half-liberated real-spheres, showing in particular that there is a bijection between the symmetric ones and the conjugation stable closed subspaces of the complex projective spaces.Comment: 10 page

Hopf-Galois Systems

We introduce the concept of Hopf-Galois system, a reformulation of the notion of Galois extension of the base field for a Hopf algebra. The main feature of our definition is a generalization of the antipode of an ordinary Hopf algebra. The main application of Hopf-Galois systems is the construction of monoidal equivalences between comodule categories over Hopf algebras.Comment: 15 page

Galois reconstruction of finite quantum groups

We describe a universal factorization for a functor with values in finite-dimensional measured algebras. More precisely we contruct the quantum automorphism group of this functor. This general recontruction result allows us to recapture a finite-dimensional Hopf algebra from the category of finite-dimensional measured comodule algebras.Comment: Latex, 10 page

Quotients and Hopf Images of a Smash Coproduct

We describe the Hopf algebra quotients and Hopf images of the smash coproduct of a group algebra by the algebra of functions on a finite group.Comment: 17 page