There are many ways to extend the ideas of classical differential geometry to a
noncommutative world. Our view is that there is no clear answer as to which of these is …

We introduce the notion of 'bar category'by which we mean a monoidal category equipped
with additional structure formalising the notion of complex conjugation. Examples of our …

We recall the notion of Hopf quasigroups introduced previously. We construct a
bicrossproduct Hopf quasigroup $ kM\bicross k (G) $ from every group $ X $ with a finite …

Frobenius--Schur indicators for a class of fusion categories Page 1 Pacific Journal of
Mathematics FROBENIUS–SCHUR INDICATORS FOR A CLASS OF FUSION …

We provide a systematic treatment of boundaries based on subgroups K⊆ G for the Kitaev
quantum double D (G) model in the bulk. The boundary sites are representations of a∗ …

Given a fusion category\mathcal CC and an indecomposable\mathcal C C-module
category\mathcal MM, the fusion category\mathcal C^* _ _\mathcal M CM∗ of\mathcal C C …

We show that the double 𝒟 of the nontrivially associated tensor category constructed from
left coset representatives of a subgroup of a finite group X is a modular category. Also we …

In this work, we use the concept of G-weak graded rings and G-weak graded modules,
which are based on grading by a set G of left coset representatives for the left action of a …

Let R be an associative ring with unity, X be a finite group, H be a subgroup of X, and G be a
set of left coset representatives for the left action of H on X. In this article, we introduce two …

In this article, we generalize the concept of group-graded modules by introducing the
concept of G-weak graded R-modules, which are R-modules graded by a set G of left coset …