Representations of tensor categories coming from quantum linear spaces

Exact indecomposable module categories over the tensor category of representations of Hopf algebras that are liftings of quantum linear spaces are classified.Comment: 21 pages. Some minor mistakes are corrected. Section 4.1 is new. To appear in the Journal of the London Mathematical Societ

Dynamical twists in Hopf algebras

We establish a bijective correspondence between gauge equivalence classes of dynamical twists in a finite-dimensional Hopf algebra $H$ based on a finite abelian group $A$ and equivalence classes of pairs $(K, \{V_{\lambda}\}_{\lambda\in \hat{A}})$, where $K$ is an $H$-simple left $H$-comodule semisimple algebra and $\{V_{\lambda}\}_{\lambda\in \hat{A}}$ is a family of irreducible representations satisfying certain conditions. Our results generalize the results obtained by Etingof-Nikshych on the classification of dynamical twists in group algebras.Comment: 21 pages, minor misprints corrected, to appear in Int. Math. Res. No

Crossed extensions of the corepresentation category of finite supergroup algebras

We present explicit examples finite tensor categories that are C_2-graded extensions of the corepresentation category of certain finite-dimensional non-semisimple Hopf algebras.Comment: 26 pages. An error in the product given in definition 4.7 was correcte