Related papers: Paravortices: loop braid representations with both…
Let $\Lambda$ be a finite-dimensional associative algebra. The torsion classes of $mod\, \Lambda$ form a lattice under containment, denoted by $tors\, \Lambda$. In this paper, we characterize the cover relations in $tors\, \Lambda$ by…
We classify globally irreducible representations of alternating groups and double covers of symmetric and alternating groups. In order to achieve this classification we also completely characterise irreducible representations of such groups…
The spin network quantum simulator relies on the su(2) representation ring (or its q-deformed counterpart at q= root of unity) and its basic features naturally include (multipartite) entanglement and braiding. In particular, q-deformed spin…
Maximal parabolic subalgebras of untwisted affine Kac-Moody algebras were studied in the context of Borel-de Siebenthal theory in [13], where they were realized as certain equivariant map algebras with a non-free abelian group action. In…
We consider a framework for representing double loop spaces (and more generally E-2 spaces) as commutative monoids. There are analogous commutative rectifications of braided monoidal structures and we use this framework to define iterated…
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-$N$…
Double-bosonisation associates to a braided group in the category of modules of a quantum group, a new quantum group. We announce the semiclassical version of this inductive construction.
Recent work suggests that topological features of certain quantum gravity theories can be interpreted as particles, matching the known fermions and bosons of the first generation in the Standard Model. This is achieved by identifying…
In this thesis, we develop the theory of bifibrations of polycategories. We start by studying how to express certain categorical structures as universal properties by generalising the shape of morphism. We call this phenomenon…
We relate commutative algebras in braided tensor categories to braid-reversed tensor equivalences, motivated by vertex algebra representation theory. First, for $\mathcal{C}$ a braided tensor category, we give a detailed construction of the…
The notion of shifted quantum groups has recently played an important role in algebraic geometry. This subtle modification of the original definition brings more flexibility in the representation theory of quantum groups. The first part of…
Using the recoupling theory, we define a representation of the pure braid group and show that it is not trivial.
Important characteristics of the loop approach to quantum gravity are a specific choice of the algebra A of observables and of a representation of A on a measure space over the space of generalized connections. This representation is…
We develop a theory of localization for braid group representations associated with objects in braided fusion categories and, more generally, to Yang-Baxter operators in monoidal categories. The essential problem is to determine when a…
The inclusion of the unit in a braided tensor category $\mathcal{V}$ induces a 1-morphism in the Morita 4-category of braided tensor categories $BrTens$. We give criteria for the dualizability of this morphism. When $\mathcal{V}$ is a…
The discussions in the present paper arise from exploring intrinsically the structure nature of the quantum $n$-space. A kind of braided category $\Cal {GB}$ of $\La$-graded $\th$-commutative associative algebras over a field $k$ is…
A long-term research proposal on the algebraic structure, the representations and the possible applications of paraparticle algebras is structured in three modules: The first part stems from an attempt to classify the inequivalent gradings…
A monoid structure on families of representations of a quiver is introduced by taking extensions of representations in families, i.e. subvarieties of the varieties of representations. The study of this monoid leads to interesting…
Various properties of a class of braid matrices, presented before, are studied considering $N^2 \times N^2 (N=3,4,...)$ vector representations for two subclasses. For $q=1$ the matrices are nontrivial. Triangularity $(\hat R^2 =I)$…
We give a simple topological construction of the Burau representations of the loop braid groups. There are four versions: defined either on the non-extended or extended loop braid groups, and in each case there is an unreduced and a reduced…