In this paper it is proved that the pure braided Thompson’s group BF admits a bi-order, analog to the bi-order of the pure braid groups.

For an abelian group $A$, we study a close connection between braided $A$-crossed tensor categories with trivialization of the $A$-action and $A$-graded categories. Additionally, prove that obstruction to existence categorical action $T$ on category $\mathcal{C}$ is given by element $O(T) \in H^2(G, \operatorname{Aut}_{\otimes}(\operatorname{Id}_{\mathcal{C}}))$. In case = 0$, set obstructions ...

A new deformation of the of the Poincaré group and of the Minkowski space-time is given. From the mathematical point of view this deformation is rather quantum-braided group. Global and local structure of this quantumbraided Poincaré group is investigated. A kind of “quantum metrics” is introduced in the q-Minkowski space.

The constraints of a monoidal category are too strong for some applications in physics. Although the natural isomorphism property is founded on strong physical principles (see Joyce [2]) there are no conclusive grounds for requiring that the pentagon and triangle diagrams hold. For example in Joyce [4,5] recouplings embodying the Pauli exclusion principle are natural isomorphisms that do not sa...

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 associativity and commutativity morphisms. 1. Results We consider near-group categories; that is, semisimple monoidal categories, whose set of simples consists ...

We describe a method for quantization of Poisson Hopf algebras in Q-linear symmetric monoidal categories. It is compatible with tensor products and can also be used to produce braided algebras. The main idea comes from the fact that nerves groups are simplicial sets. Nerves then turn out rather than infinitesimally braided. problem thus solved via standard machinery Drinfeld associators.

We consider an inductive scheme for quantized enveloping algebras, arising from certain inclusions of the associated root data. These inclusions determine an algebra-subalgebra pair with the subalgebra also a quantized enveloping algebra, and we want to understand the structure of the “difference” between the algebra and the subalgebra. Our point of view treats the background field and quantiza...

Discrete subfactors include a particular class of infinite index and all finite ones. A discrete subfactor is called local when it braided fulfills commutativity condition motivated by the study inclusion Quantum Field Theories in algebraic Haag–Kastler setting. In Bischoff et al. (J Funct Anal 281(1):109004, 2021), we proved that every irreducible arises as fixed point under action canonical c...

Suture performances include handling characteristics and knot mechanical properties. These performances depend mainly on frictional, flexural, and compressive forces. The interaction between these forces developed inside the suture knot governs the displacement mode and the deformability of the suture yarn inside the knot. In the present work, we studied the effect of manufacturing conditions o...