相关论文: Double Centralizers of Parabolic Subgroups of Brai…
Let $G$ be a group endowed with a solution to the conjugacy problem and with an algorithm which computes the centralizer in $G$ of any element of $G$. Let $H$ be a subgroup of $G$. We give some conditions on $H$, under which we provide a…
We give a new method to compute the centralizer of an element in Artin braid groups and, more generally, in Garside groups. This method, together with the solution of the conugacy problem given by the authors in a previous paper, are two…
We provide the first solution to the double coset problem (DCP) for a large class of natural subgroups of braid groups, namely for all parabolic subgroups which have a connected associated Coxeter graph. Update: We succeeded to solve the…
We provide a general formula for Mueger's centralizer of any fusion subcategory of a braided fusion category containing a tannakian subcategory. This entails a description for Mueger's centralizer of all fusion subcategories of a group…
Let $W$ be an arbitrary Coxeter group, possibly of infinite rank. We describe a decomposition of the centralizer $Z_W(W_I)$ of an arbitrary parabolic subgroup $W_I$ into the center of $W_I$, a Coxeter group and a subgroup defined by a…
We introduce and investigate the ribbon groupoid associated with a Garside group. Under a technical hypothesis, we prove that this category is a Garside groupoid. We decompose this groupoid into a semi-direct product of two of its parabolic…
We study the centralizer of a braid from the point of view of Garside theory, showing that generically a minimal set of generators can be computed very efficiently, as the ultra summit set of a generic braid has a very particular structure.…
The mixed braid groups are the subgroups of Artin braid groups whose elements preserve a given partition of the base points. We prove that the centralizer of any braid can be expressed in terms of semidirect and direct products of mixed…
In this paper we introduce a class of `parabolic' subgroups for the generalized braid group associated to an arbitrary irreducible complex reflection group, which maps onto the collection of parabolic subgroups of the reflection group.…
How far can the elementary description of centralizers of parabolic subalgebras of Hecke algebras of finite real reflection groups be generalized to the complex reflection group case? In this paper we begin to answer this question by…
In this article, we investigate monoidal, braided, sylleptic centralizers of monoidal, braided, sylleptic 2-functors. We specifically focus on multifusion 2-categories and show that monoidal, braided, sylleptic centralizers are multifusion…
Let S be a finite graph and G be the corresponding free partially commutative group. In this paper we study subgroups generated by vertices of the graph S, which we call canonical parabolic subgroups. A natural extension of the definition…
We determine all finite subgroups of simple algebraic groups that have irreducible centralizers - that is, centralizers whose connected component does not lie in a parabolic subgroup.
We give characterizations of the center, of conjugated and of commuting elements in a fundamental group of a graph of group. We deduce various results : on the one hand we give a sufficient condition for the center, the centralizers, and…
In this note, we provide a (super-exponential time) algorithm to solve the generalized conjugacy problem in relatively hyperbolic groups, given solvability of the generalized conjugacy problem in each of the parabolic subgroups.
Consider a relatively hyperbolic group G. We prove that if G is finitely presented, so are its parabolic subgroups. Moreover, a presentation of the parabolic subgroups can be found algorithmically from a presentation of G, a solution of its…
We study special subgroups of infinite groups that generalize double centralizers. We analyze sufficient conditions for descending chains of such subgroups to stop after finitely many steps. We discuss whether this phenomenon can happen in…
We give a complete classification of conjugacy stable parabolic subgroups of Artin-Tits groups of spherical type. This answers a question posed by Ivan Marin and generalizes a theorem obtained by Juan Gonz\'alez-Meneses in the specific case…
In this note we solve the twisted conjugacy problem for braid groups, i.e. we propose an algorithm which, given two braids $u,v\in B_n$ and an automorphism $\phi \in Aut (B_n)$, decides whether $v=(\phi (x))^{-1}ux$ for some $x\in B_n$. As…
This text brings to an end the classification of non-reduced parabolic subgroups in positive characteristic, especially two and three: they are all obtained as intersections of parabolics having maximal reduced part. We prove this result…