Related papers: Twisted Virtual Braid Group

Nonuniqueness of semidirect decompositions of groups is an insufficiently studied question in contrast to direct decompositions. We obtain some results about semidirect decompositions for semidirect products with factors which are…

The topological classification of energy bands has laid the groundwork for the discovery of various topological phases of matter in recent decades. While this classification has traditionally focused on real-energy bands, recent studies…

Let $\sigma\colon G \to S_n$ be a surjective homomorphism and let $H$ be a group. We introduce the \emph{permutational wreath pullback} \[ H \wr_\sigma G = H^n \rtimes_\sigma G, \] where the action of $G$ on $H^n$ is induced by permutation…

We construct braid group actions on coideal subalgebras of quantized enveloping algebras which appear in the theory of quantum symmetric pairs. In particular, we construct an action of the semidirect product of Z^n and the classical braid…

In the present paper, we construct a monomorphism from (Artin) pure braid group $PB_{n}$ into a group, which is `bigger' than $PB_{n}$. Roughly speaking, this mapping is defined on words of braids by adding `new generators' between…

In this paper, we investigate the structure of the automorphism groups of pure braid groups. We prove that, for $n>3$, $\Aut(P_n)$ is generated by the subgroup $\Aut_c(P_n)$ of central automorphisms of $P_n$, the subgroup $\Aut(B_n)$ of…

We introduce the notion of a braid group parametrized by a ring, which is defined by generators and relations and based on the geometric idea of painted braids. We show that the parametrized braid group is isomorphic to the semi-direct…

For a quasitriangular C*-quantum group, we enrich the twisted tensor product constructed in the first part of this series to a monoidal structure on the category of its continuous coactions on C*-algebras. We define braided C*-quantum…

We introduce an axiomatization of the notion of a semidirect product of locally compact quantum groups and study properties. Our approach is slightly different from the one introduced in the thesis of S.~Roy and, unlike the investigations…

We construct braided versions $sV_{br}$ of the Brin-Thompson groups $sV$ and prove that they are of type $F_\infty$. The proof involves showing that the matching complexes of colored arcs on surfaces are highly connected.

We introduce a definition of braided tensor product $\operatorname{M}\overline{\boxtimes}\operatorname{N}$ of von Neumann algebras equipped with an action of a quasi-triangular quantum group $\mathbb{G}$ (this includes the case when…

We investigate the braid group representations arising from categories of representations of twisted quantum doubles of finite groups. For these categories, we show that the resulting braid group representations always factor through finite…

In this paper, we study the asymptotics of several growth functions related to twisted conjugacy on virtually abelian groups. First, we study the twisted conjugacy growth function, which counts the number of twisted conjugacy classes…

We introduce linear representations of the universal virtual braid group $UV_n(c)$, where $n\geq 2$ and $c\geq 1$, which is a unifying framework for braid-type groups with multiple types of crossings. We classify and study its complex…

Virtual knots arise in the study of Gauss diagrams and Vassiliev invariants of usual knots. Virtual braids correspond naturally to virtual knots. We consider the group of virtual braids on n strings VB_n and its Burau representation, in…

We study the notion of $1$-twisted semi-homogeneous vector bundles on $\mathbb{G}_m$-gerbes over abelian varieties, and classify point objects in the twisted derived categories of abelian varieties. As an application, we classify the…

We define pseudo-Garside groups and prove a theorem about them parallel to Garside's result on the word problem for the usual braid groups. The main novelty is that the set of simple elements can be infinite. We introduce a group B=B(Z^n)…

We apply Majid's transmutation procedure to Hopf algebra maps $H \to \mathbb C[T]$, where $T$ is a compact abelian group, and explain how this construction gives rise to braided Hopf algebras over quotients of $T$ by subgroups that are…

We construct the complete invariant for fused links. It is proved that the set of equivalence classes of $n$-component fused links is in one-to-one correspondence with the set of elements of the abelization $UVP_n/UVP_n^{\prime}$ up to…

The virtual knot theory is a new interesting subject in the recent study of low dimensional topology. In this paper, we explore the algebraic structure underlying the virtual braid group and call it the virtual Temperley--Lieb algebra which…