Search results for "braid groups"
showing 6 items of 6 documents
Categorical action of the extended braid group of affine type $A$
2017
Using a quiver algebra of a cyclic quiver, we construct a faithful categorical action of the extended braid group of affine type A on its bounded homotopy category of finitely generated projective modules. The algebra is trigraded and we identify the trigraded dimensions of the space of morphisms of this category with intersection numbers coming from the topological origin of the group.
A note on the Lawrence-Krammer-Bigelow representation
2002
A very popular problem on braid groups has recently been solved by Bigelow and Krammer, namely, they have found a faithful linear representation for the braid group B_n. In their papers, Bigelow and Krammer suggested that their representation is the monodromy representation of a certain fibration. Our goal in this paper is to understand this monodromy representation using standard tools from the theory of hyperplane arrangements. In particular, we prove that the representation of Bigelow and Krammer is a sub-representation of the monodromy representation which we consider, but that it cannot be the whole representation.
MR 2776821 Reviewed Berger E. Hurwitz equivalence in dihedral groups. The Electronic Journal of Combinatorics 18 (2011), no.1, paper 45, 16 pp. (Revi…
2011
In the paper under review, the author studies the orbits of the action of the braid group B_{n} on G^{n} where G denoted a dihedral group. At first, the author considers tuples T consisting only of reflections. In this case, the author proves that the orbits are determinate by three invariants. These invariants are the product of the entries, the subgroup generated by the entries and the number of times each conjugacy class is represented in T. Successively, the author works with tuples whose entries are any elements of dihedral groups. The author shows that, also this time, the above invariants are sufficient in order to determinate the orbits of the action of B_{n} on G^{n}.
The HOMFLY-PT polynomials of sublinks and the Yokonuma–Hecke algebras
2016
We describe completely the link invariants constructed using Markov traces on the Yokonuma-Hecke algebras in terms of the linking matrix and the HOMFLYPT polynomials of sublinks.
MR 3020148 Reviewed McMullen, C.T. Braid groups and Hodge theory. Mathematische Annalen, vol. 355 (2013), pp.893–-946. (Reviewer Francesca Vetro) 20F…
2014
In this paper, the author studies the unitary representations of the braid group and the geometric structures on moduli space that arise via the Hodge theory of cyclic branched coverings of P^1. In particular, the author is interested in the classification of certain arithmetic subgroups of U(r, s) which envelop the image of the braid group. The author investigates their connections with complex reflection groups, Teichm\"{u}lller curves, ergodic theory and problems in surface topology.
Conjugacy problem for braid groups and Garside groups
2003
We present a new algorithm to solve the conjugacy problem in Artin braid groups, which is faster than the one presented by Birman, Ko and Lee. This algorithm can be applied not only to braid groups, but to all Garside groups (which include finite type Artin groups and torus knot groups among others).