Related papers: On the braid group representations coming from wea…
We investigate a family of (reducible) representations of Artin's braid groups corresponding to a specific solution to the Yang-Baxter equation. The images of the braid groups under these representations are finite groups, and we identify…
We show that representations of the loop braid group arise from Aharonov-Bohm like effects in finite 2-group (3+1)-dimensional topological higher gauge theory. For this we introduce a minimal categorification of biracks, which we call…
We use some Lie group theory and Budney's unitarization of the Lawrence-Krammer representation, to prove that for generic parameters of definite form the image of the representation (also on certain types of subgroups) is dense in the…
We give a method to produce representations of the braid group $B_n$ of $n-1$ generators ($n\leq \infty$). Moreover, we give sufficient conditions over a non unitary representation for being of this type. This method produces examples of…
We classify Lagrangian subcategories of the representation category of a twisted quantum double of a finite group. In view of results of 0704.0195v2 this gives a complete description of all braided tensor equivalent pairs of twisted quantum…
We prove a characterization of monomial projective representations of finitely generated nilpotent groups. We also characterize polycyclic groups whose projective representations are finite dimensional.
In this paper, using some properties of fundamental groups and covering spaces of connected polyhedra and CW-complexes, we present topological proof for some famous theorems about finitely presented groups.
We consider subgroups of the braid groups which are generated by $k$-th powers of the standard generators and prove that any infinite intersection (with even $k$) is trivial. This is motivated by some conjectures of Squier concerning the…
Artin groups of finite type are not as well understood as braid groups. This is due to the additional geometric properties of braid groups coming from their close connection to mapping class groups. For each Artin group of finite type, we…
We define an action of Artin's braid group on a finite dimensional algebra.
We survey several notions of Mackey functors and biset functors found in the literature and prove some old and new theorems comparing them. While little here will surprise the experts, we draw a conceptual and unified picture by making…
In this article we give an elementary introduction to the representation theory of finite magnetic groups from a purely mathematical point of view. -- En este art\'iculo damos una introducci\'on elemental a la teor\'ia de representaciones…
We prove that braid group representations associated to braided fusion categories and mapping class group representations associated to modular fusion categories are always semisimple. The proof relies on the theory of extensions in…
We show that any slightly degenerate weakly group-theoretical fusion category admits a minimal non-degenerate extension. Let $d$ be a positive square-free integer, given a weakly group-theoretical non-degenerate fusion category…
Generalized Yang-Baxter matrices sometimes give rise to braid group representations. We identify the exact images of some qubit representations of the braid groups from generalized Yang-Baxter matrices obtained from anyons in the…
We study unitary representations of semidirect products of a compact quantum group with a finite group. We give a classification of all irreducible unitary representations, a description of the conjugate representation of irreducible…
A large class of positive finite presentations of the braid groups is found and studied. It is shown that no presentations but known exceptions in this class have the property that equivalent braid words are also equivalent under positive…
We introduce a weakening of the notion of fusion 2-category given in arXiv:1812.11933. Then, we establish a number of properties of (multi)fusion 2-categories. Finally, we describe the fusion rule of the fusion 2-categories associated to…
We show that if a group can be represented as a graph product of finite directly indecomposable groups, then this representation is unique.
In this paper we study the relative tensor product of module categories over braided fusion categories using, in part, the notion of the relative center of a module category. In particular we investigate the canonical tensor category…