We will present a notion of (pre)torsion theory in general categories and two interesting examples of such pretorsion theories. Torsion theories in arbitrary categories have been studied by Grandis, Janelidze, Márki and several others. Our main examples will be in the category of preordered sets and the category of finite algebras with one operation, unary, and no axioms (i.e., the category of...
The Galois theory for monoidal cowreaths is developed. Cleft cowreaths are introduced in this context and its relation with the normal basis property investigated. The connection of this class of cowreath with some wreath algebra structures is obtained. Finally, several applications to quasi-Hopf algebras will be discussed. This is a joint work with D. Bulacu.
In this talk we deal with Hopf Ore extensions, the role they play in the classification of low dimensional Hopf algebras, and the property of a Hopf algebra to be almost involutive (meaning that the square of the antipode has a square root that is an automorphism of Hopf algebras).
