Using a variety of methods developed in the literature (in particular, the theory of weak Hopf
algebras), we prove a number of general results about fusion categories in characteristic …

A two-sided coaction of a Hopf algebra on an associative algebra ℳ is an algebra map of the
form, where (λ, ρ) is a commuting pair of left and right-coactions on ℳ, respectively. Denoting …

We construct a large family of ribbon quasi-Hopf algebras related to small quantum groups,
with a factorizable R-matrix. Our main purpose is to obtain non-semisimple modular tensor …

We provide a complete classification of fusion categories of Frobenius-Perron (FP)
dimension pq over complex numbers, where p< q are distinct primes, thus giving a …

These are the lecture notes for a short course on tensor categories. The coverage in these
notes is relatively non-technical, focussing on the essential ideas. They are meant to be …

We generalize the fundamental structure Theorem on Hopf (bi)-modules by Larson and
Sweedler to quasi-Hopf algebras H. If H is finite dimensional this proves the existence and …

In this paper, we define the higher Frobenius-Schur (FS-) indicators for finite-dimensional
modules of a semisimple quasi-Hopf algebra $ H $ via the categorical counterpart …

A classical result in the theory of Hopf algebras concerns the uniqueness and existence of
integrals: for an arbitrary Hopf algebra, the integral space has dimension⩽ 1, and for a finite …

The construct, ion of quasi-Hopf algebras obtains its importance from its signficance in
Physics, cf.[l], 151, 161. Since for usual quantum groups and Hopf algebras actions and …

In this paper, we obtain a canonical central element νH for each semi-simple quasi-Hopf
algebra H over any field k and prove that νH is invariant under gauge transformations. We …