Related papers: Galois Theory for Braided Tensor Categories and th…

We define a Galois structure on the category of pairs of equivalence relations in an exact Mal'tsev category, and characterize central and double central extensions in terms of higher commutator conditions. These results generalize both the…

Using the tensor category theory developed by Lepowsky, Zhang and the second author, we construct a braided tensor category structure with a twist on a semisimple category of modules for an affine Lie algebra at an admissible level. We…

In this paper, we study modular categories whose Galois group actions on their simple objects are transitive. We show that such modular categories admit unique factorization into prime transitive factors. The representations of…

We study the module category of a certain Galois covering of a cluster-tilted algebra which we call the cluster repetitive algebra. Our main result compares the module categories of the cluster repetitive algebra of a tilted algebra C and…

We explore the relationship between the category of MV-algebras and its full subcategories of perfect and semisimple algebras, showing that this pair of subcategories defines a pretorsion theory. We study the Galois structure associated…

This paper is the first of a pair that aims to classify a large number of the type $II$ quantum subgroups of the categories $\mathcal{C}(\mathfrak{sl}_{r+1},k)$. In this work we classify the braided auto-equivalences of the categories of…

A C*-tensor category with simple unit object is realized by von Neumann algebra bimodules of finite Jones index if and only if it is rigid.

In the context of internal crossed modules over a fixed base object in a given semi-abelian category, we use the non-abelian tensor product in order to prove that an object is perfect (in an appropriate sense) if and only if it admits a…

We give a new sufficient condition for the normal extensions in an admissible Galois structure to be reflective. We then show that this condition is indeed fulfilled when X is the (protomodular) reflective subcategory of S-special objects…

We study Galois extensions Coinv(M)<M for M an H-comodule algebra and H a Frobenius Hopf algebroid. We obtain generalizations of various theorems in Hopf-Galois theory by Kreimer-Takeuchi, Doi-Takeuchi and Cohen-Fischman-Montgomery. An…

Sect 1 introduces Nielsen classes attached to (G,C), where C is r conjugacy classes in a finite group G, and a braid action on them. These give reduced Hurwitz spaces, denoted H(G,C)^rd. The section concludes with a braid formula for the…

We classify the finite groups $G$ which satisfies the condition that every complex irreducible character,whose degree's square doesn't divide the index of its kernel in $G$, lies in the same Galois conjugacy class.

A two-dimensional chiral conformal field theory can be viewed mathematically as the representation theory of its chiral algebra, a vertex operator algebra. Vertex operator algebras are especially well suited for studying logarithmic…

Graded-division algebras are building blocks in the theory of finite-dimensional associative algebras graded by a group G. If G is abelian, they can be described, using a loop construction, in terms of central simple graded-division…

We construct projective covers of irreducible V-modules in the category of grading-restricted generalized V-modules when V is a vertex operator algebra satisfying the following conditions: 1. V is C_{1}-cofinite in the sense of Li. 2. There…

We show that there exists a Galois correspondence between subalgebras of an H-comodule algebra A over a base ring R and generalised quotients of a Hopf algebra H. We also show that Q-Galois subextensions are closed elements of the…

We construct several new classes of bifunctors $(A,B)\mapsto A\otimes_{\alpha} B$, where $A\otimes_\alpha B$ is a cross norm completion of $A\odot B$ for each pair of C*-algebras $A$ and $B$. For the first class of bifunctors considered…

This paper introduces the concept of distorted monoidal categories, a generalization of monoidal and braided monoidal categories that supports non-reversible and direction-sensitive tensor structures. Unlike the classical setting, where the…

Fusion categories are fundamental objects in quantum algebra, but their definition is narrow in some respects. By definition a fusion category must be k-linear for some field k, and every simple object V is strongly simple, meaning that (V)…

We investigate a class of combinatory algebras, called ribbon combinatory algebras, in which we can interpret both the braided untyped linear lambda calculus and framed oriented tangles. Any reflexive object in a ribbon category gives rise…