Related papers: Braid groups of imprimitive complex reflection gro…

We find finite presentations for the automorphism group of the Artin pure braid group and the automorphism group of the pure braid group associated to the full monomial group.

This is the last of three papers on Drinfeld presentations of quasi-split affine iquantum groups $\widetilde{{\mathbf U}}^\imath$, settling the remaining type ${\rm AIII}^{(\tau)}_{2r}$. This type distinguishes itself among all quasi-split…

This paper gives a new, simplified presentation of the classical pure braid group. The generators are given by the squares of the longest elements over connected subgraphs, and we prove that the only relations are either commutators or…

In this paper, we will seek appropriate generators to define the characteristic polynomials of $G(r,1,n)$, and prove that for every finite dimensional representation of $G(r,1,n)$, the characteristic polynomial of $G(r,1,n)$ determines the…

Let G be the fundamental group of the complement of a K(G,1) hyperplane arrangement (such as Artin's pure braid group) or more generally a homologically toroidal group (as defined in the paper). The subgroup of elements in the complex…

We give several new positive finite presentations for the pure braid group that are easy to remember and simple in form. All of our presentations involve a metric on the punctured disc so that the punctures are arranged "convexly", which is…

In this article, we introduce a new family of groups, called Chambord groups and constructed from braided strand diagrams associated to specific semigroup presentations. It includes the asymptotically rigid mapping class groups previously…

We give a complete classification of simple representations of the braid group B_3 with dimension $\leq 5$ over any algebraically closed f ield. In particular, we prove that a simple d-dimensional representation $\rho: B_3 \to GL(V)$ is…

This article extends the works of Gon\c{c}alves, Guaschi, Ocampo [GGO] and Marin [MAR2] on finite subgroups of the quotients of generalized braid groups by the derived subgroup of their pure braid group. We get explicit criteria for…

We investigate a new lattice of generalised non-crossing partitions, constructed using the geometry of the complex reflection group $G(e,e,r)$. For the particular case $e=2$ (resp. $r=2$), our lattice coincides with the lattice of simple…

We investigate the rational cohomology of the quotient of (generalized) braid groups by the commutator subgroup of the pure braid groups. We provide a combinatorial description of it using isomorphism classes of certain families of graphs.…

In his proof of the K(pi,1) conjecture for complex reflection arrangements, Bessis defined Garside categories suitable for studying braid groups of centralizers of Springer regular elements in well-generated complex reflection groups. We…

Brou\'e, Malle and Rouquier conjectured in that the center of the pure braid group of an irreducible finite complex reflection group is cyclic. We prove this conjecture, for the remaining exceptional types, using the analogous result for…

We consider quotients of the group algebra of the $3$-string braid group $B_3$ by $p$-th order generic polynomial relations on the elementary braids. In cases $p=2,3,4,5$ these quotient algebras are finite dimensional. We give…

Birman, Ko and Lee have introduced a new monoid ${\cal B}^{*}_{n}$--with an explicit presentation--whose group of fractions is the $n$-strand braid group ${\cal B}_{n}$. Building on a new approach by Digne, Michel and himself, Bessis has…

Complex braid groups are the natural generalizations of braid groups associated to arbitrary (finite) complex reflection groups. We investigate several methods for computing the homology of these groups. In particular, we get the Poincar\'e…

We show that braided Cherednik algebras introduced by the first two authors are cocycle twists of rational Cherednik algebras of the imprimitive complex reflection groups $G(m,p,n)$, when $m$ is even. This gives a new construction of mystic…

We define the braid groups of a two-dimensional orbifold and introduce conventions for drawing braid pictures. We use these to realize the Artin groups associated to the spherical Coxeter diagrams A_n, B_n=C_n and D_n and the affine…

We define and study extensions of Artin's representation and braid monodromy representation to the case of topological and algebraical generalisations of braid groups. In particular we provide faithful representations of braid groups of…

This paper studies quantum symmetric pairs $(\widetilde{\mathbf U}, \widetilde{{\mathbf U}}^\imath )$ associated with quasi-split Satake diagrams of affine type $A_{2r-1}, D_r, E_{6}$ with a nontrivial diagram involution fixing the affine…