Related papers: Generalized and quasi-localizations of braid group…

Governed by locality, we explore a connection between unitary braid group representations associated to a unitary $R$-matrix and to a simple object in a unitary braided fusion category. Unitary $R$-matrices, namely unitary solutions to the…

We study categories whose objects are the braid representations, i.e. strict monoidal functors $F\colon B\rightarrow Mat$ from the braid category $B$ to the category of matrices $Mat$. Braid representations are equivalent to solutions to…

Inspired by quantum information theory, we look for representations of the braid groups $B_n$ on $V^{\otimes (n+m-2)}$ for some fixed vector space $V$ such that each braid generator $\sigma_i, i=1,...,n-1,$ acts on $m$ consecutive tensor…

We investigate braid group representations associated with unitary braided vector spaces, focusing on a conjecture that such representations should have virtually abelian images in general and finite image provided the braiding has finite…

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 initiate the systematic study of modular representations of symmetric groups that arise via the braiding in (symmetric) tensor categories over fields of positive characteristic. We determine what representations appear for certain…

Braid groups are an important and flexible tool used in several areas of science, such as Knot Theory (Alexander's theorem), Mathematical Physics (Yang-Baxter's equation) and Algebraic Geometry (monodromy invariants). In this note we will…

Supersymmetry algebras can be used to obtain algebraic expressions for constant Yang-Baxter solutions, also known as braid group generators. This was done for non-invertible braid operators in \cite{maity2025non}. In this work we extend…

We use the theory of regular objects in tensor categories to clarify the passage between braided multiplicative unitaries and multiplicative unitaries with projection. The braided multiplicative unitary and its semidirect product…

We give a description of the centralizer algebras for tensor powers of spin objects in the pre-modular categories $SO(N)_2$ (for $N$ odd) and $O(N)_2$ (for $N$ even) in terms of quantum $(n-1)$-tori, via non-standard deformations of…

The paper extends the notion of braided set and its close relative - the Yang-Baxter set - to the category of vector spaces and explore structure aspects of such a notion as morphisms and extensions. In this way we describe a family of…

We define quasi--locally presentable categories as big unions of coreflective subcategories which are locally presentable. Under appropriate hypotheses we prove a representability theorem for exact contravariant functors defined on a…

Loop braid groups characterize the exchange of extended objects, namely loops, in three dimensional space generalizing the notion of braid groups that describe the exchange of point particles in two dimensional space. Their interest in…

We study a wide range of homologically-defined representations of surface braid groups and of mapping class groups of surfaces, including the Lawrence-Bigelow representations of the classical braid groups. These representations naturally…

This work presents an approach towards the representation theory of the braid groups $B_n$. We focus on finite-dimensional representations over the field of Laurent series which can be obtained from representations of infinitesimal braids,…

A near-group category is an additively semisimple category with a product such that all but one of the simple objects is invertible. We classify braided structures on near-group categories, and give explicit numerical formulas for their…

In this paper we present reducible representation of the $n^{2}$ braid group representation which is constructed on the tensor product of n-dimensional spaces. By some combining methods we can construct more arbitrary $n^{2}$ dimensional…

The notion of a glider representation of a chain of normal subgroups of a group is defined by a new structure, i.e. a fragment for a suitable filtration on the group ring. This is a special case of general glider representations defined for…

A braid representation is a monoidal functor from the braid category $\mathsf{B}$, for example given by a solution to the constant Yang-Baxter equation. Given a monoidal category $\mathsf{C}$ with $ob(\mathsf{C})=\mathbb{N}$, a rank-$N$…

We classify braided generalized near-group fusion categories whose global dimension is not an integer; there are exactly two up to Grothendieck equivalence and taking products with braided pointed fusion categories.