Results 51 to 60 of about 2,228 (168)

CLASSIFICATION OF SYMMETRY GROUPS FOR PLANAR $n$ -BODY CHOREOGRAPHIES

Forum of Mathematics, Sigma, 2013
Since the foundational work of Chenciner and Montgomery in 2000 there has been a great deal of interest in choreographic solutions of the $n$ -body problem ...
JAMES MONTALDI, KATRINA STECKLES
doaj   +1 more source

Parametrized braid groups of Chevalley groups.

Documenta Mathematica, 2005
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 product of the Steinberg group (of the ring) with the classical braid group.
Loday, Jean-Louis, Stein, Michael R.
openaire   +2 more sources

Finite Group Factorizations and Braiding

Journal of Algebra, 1996
LATEX, 39 pages, more final ...
Beggs, E.J., Gould, J.D., Majid, S.
openaire   +3 more sources

A 3-skeleton for a classifying space for the symmetric group

Journal of Computational Algebra
We construct a 3-dimensional cell complex that is the 3-skeleton for an Eilenberg–MacLane classifying space for the symmetric group Sn. Our complex starts with the presentation for Sn with n−1 adjacent transpositions with squaring, commuting, and braid ...
Matthew B. Day, Trevor Nakamura
doaj   +1 more source

Burau representation of $B_4$ and quantization of the rational projective plane

Comptes Rendus. Mathématique
The braid group $B_4$ naturally acts on the rational projective plane $\mathbb{P}^2(\mathbb{Q})$, this action corresponds to the classical integral reduced Burau representation of $B_4$. The first result of this paper is a classification of the orbits of
Jouteur, Perrine
doaj   +1 more source

Braid Groups are Linear

The Annals of Mathematics, 2002
In a previous work [11], the author considered a representation of the braid group : B_n\to GL_m(\Bbb Z[q^{\pm 1},t^{\pm 1}]) (m=n(n-1)/2), and proved it to be faithful for n=4. Bigelow [3] then proved the same representation to be faithful for all n by a beautiful topological argument.
openaire   +2 more sources

How SU(2)$_4$ Anyons are Z$_3$ Parafermions

SciPost Physics, 2017
We consider the braid group representation which describes the non-abelian braiding statistics of the spin $1/2$ particle world lines of an SU(2)$_4$ Chern-Simons theory.
Richard Fern, Johannes Kombe, Steven H. Simon
doaj   +1 more source

Twisted virtual braid group

Journal of Knot Theory and Its Ramifications
In this paper, we study some subgroups and their decompositions in semi-direct product of the twisted virtual braid group [Formula: see text]. In particular, the twisted virtual pure braid group [Formula: see text] is the kernel of an epimorphism of [Formula: see text] onto the symmetric group [Formula: see text].
Valeriy G. Bardakov, Tatyana A. Kozlovskaya, Komal Negi, Madeti Prabhakar   +3 more
openaire   +2 more sources

Machine learning of knot topology in non-Hermitian band braids

Communications Physics
The deep connection among braids, knots and topological physics has provided valuable insights into studying topological states in various physical systems. However, identifying distinct braid groups and knot topology embedded in non-Hermitian systems is
Jiangzhi Chen, Zi Wang, Yu-Tao Tan, Ce Wang, Jie Ren   +4 more
doaj   +1 more source

Teichmüller Theory of Bordered Surfaces

Symmetry, Integrability and Geometry: Methods and Applications, 2007
We propose the graph description of Teichmüller theory of surfaces with marked points on boundary components (bordered surfaces). Introducing new parameters, we formulate this theory in terms of hyperbolic geometry.
Leonid O. Chekhov
doaj