Related papers: Positive presentations of the braid groups and the…

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.

We prove that braid group representations associated to braided fusion categories and mapping class group representations associated to modular fusion categories are always semisimple. The proof relies on the theory of extensions in…

We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…

The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. This is the second in a series of papers in…

We establish several results on the word problem for just infinite groups. First, for finitely generated just infinite groups we show that the word problem is uniformly decidable for presentations with recursively enumerable sets of…

Self-similar groups provide a rich source of groups with interesting properties; e.g., infinite torsion groups (Burnside groups) and groups with an intermediate word growth. Various self-similar groups can be described by a recursive…

In the note some construction of Lie algebras is introduced. It is proved that the construction has the same property as a well known wreath product of groups [1]: Any extension of groups can be embedded into their wreath product [2].

In this article, I introduce a group-theoretical method to prove positivity of certain linear combinations (with coefficients generally lying in $\mathbb{C}$) of exponential functions under a set of semidefinite linear constraints. The…

We obtain new presentations for the imprimitive complex reflection groups of type $(de,e,r)$ and their braid groups $B(de,e,r)$ for $d,r \ge 2$. Diagrams for these presentations are proposed. The presentations have much in common with…

We give the definition of presentations of linear monoidal categories. Our main result is that given a presentation of a linear monoidal category, we can produce a presentation of the same category as a linear category. We apply this result…

Let M be a compact, connected surface, possibly with a finite set of points removed from its interior. Let d,n be positive integers, and let N be a d-fold covering space of M. We show that the covering map induces an embedding of the n-th…

(1) There is a finitely presented group with a word problem which is a uniformly effectively inseparable equivalence relation. (2) There is a finitely generated group of computable permutations with a word problem which is a universal…

We explicitly construct an embedding of a right-angled Artin group into a classical pure braid group. Using this we obtain a number of corollaries describing embeddings of arbitrary Artin groups into right-angled Artin groups and linearly…

We exhibit a family of metrizable manifolds such that any finite group appears as the fundamental group of one of them. These spaces are especially interesting as they can be easily visualized, as opposed to classical examples of spaces…

We describe several infinite families of braided finite tensor categories. A simplest example gives a non-degenerate braided tensor category which is not Witt equivalent to a semisimple category.

In this paper, we introduce two new classes of representations of the framed braid groups. One is the homological representation constructed as the action of a mapping class group on a certain homology group. The other is the monodromy…

This article is a survey on the braid groups, the Artin groups, and the Garside groups. It is a presentation, accessible to non-experts, of various topological and algebraic aspects of these groups. It is also a report on three points of…

We study homological representations of mapping class groups, including the braid groups. These arise from the twisted homology of certain configuration spaces, and come in many different flavours. Our goal is to give a unified general…

We show that the class of representable substitution algebras is characterized by a set of universal first order sentences. In addition, it is shown that a necessary and sufficient condition for a substitution algebra to be representable is…

Irreducible Artin groups of finite type can be parametrized via their associated Coxeter diagrams into six sporadic examples and four infinite families, each of which is further parametrized by the natural numbers. Within each of these four…