Results 101 to 110 of about 321 (123)

On the linearity of Artin braid groups

Journal of Algebra, 2003
The author proves that all Artin groups of crystallographic type have a faithful representation of dimension the number of reflections of the associated Coxeter group. The faithfulness criterion which is used is that of \textit{D. Krammer} [Ann. Math. (2) 155, No. 1, 131-156 (2002; Zbl 1020.20025)].
François Digne
exaly   +2 more sources

A quotient of the Artin braid groups related to crystallographic groups

Journal of Algebra, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Daciberg Lima Gonçalves, John Guaschi, OSCAR Ocampo   +2 more
exaly   +3 more sources

Finite Hurwitz braid group actions for Artin groups

Israel Journal of Mathematics, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Stephen P Humphries, Humphries Stephen P
exaly   +2 more sources

Some subgroups of Artin's braid group

Topology and Its Applications, 1997
The braid group \(B_n\) has the presentation \[ \langle\sigma_1,\dots,\sigma_{n-1};\;\sigma_i=\sigma_j\;(|i-j|>1),\;\sigma_i\sigma_j\sigma_i=\sigma_j\sigma_i\sigma_j\;(|i-j|=1)\rangle. \] Let \(S_n\) denote the group of permutations of the set \(A_n=\{1,\dots,n\}\). There exists the standard homomorphism \(h\colon B_n\to S_n\), such that \(h(\sigma_i)=(
exaly   +3 more sources

Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups [PDF]

Algebraic and Geometric Topology, 2004
We prove by explicit construction that graph braid groups and most surface groups can be embedded in a natural way in right-angled Artin groups, and we point out some consequences of these embedding results. We also show that every right-angled Artin group can be embedded in a pure surface braid group. On the other hand, by generalising to right-angled
John Crisp, Bert Wiest, Wiest Bert
exaly   +4 more sources

On braid groups and right-angled Artin groups [PDF]

Geometriae Dedicata, 2014
A \textit{right-angled Artin group} is a group with a presentation whose only relators are commutators between generators. A. Abrams and R. Ghrist conjectured in [\textit{A. Abrams}, Geom. Dedicata 92, 185--194 (2002; Zbl 1049.20023)] and [\textit{R. Ghrist}, AMS/IP Stud. Adv. Math.
Connolly, Francis, Doig, Margaret
exaly   +3 more sources

Embedding right-angled Artin groups into graph braid groups [PDF]

Geometriae Dedicata, 2006
We construct an embedding of any right-angled Artin group $G(Δ)$ defined by a graph $Δ$ into a graph braid group. The number of strands required for the braid group is equal to the chromatic number of $Δ$. This construction yields an example of a hyperbolic surface subgroup embedded in a two strand planar graph braid group.
exaly   +3 more sources

Examples of Large Centralizers in the Artin Braid Groups

Geometriae Dedicata, 2004
N. Franco and J. González-Meneses made the following conjecture: The normalizer of an element of the Artin braid group \(B_n\) on \(n\) strings is generated by no more than \(n-1\) elements. The `normalizer' of an element of a group is defined as the subgroup of all elements commuting with it; this subgroup is often also called the `centralizer' of the
Nikolai V Ivanov
exaly   +2 more sources

Markov and Artin Normal Form Theorem for Braid Groups∗ [PDF]

Communications in Algebra, 2007
In this paper we will present the results of Artin–Markov on braid groups by using the Gröbner–Shirshov basis. As a consequence we can reobtain the normal form of Artin–Markov–Ivanovsky as an easy corollary.
Leonid A. Bokut, V. V. Chaynikov, Kar Ping Shum   +2 more
exaly   +4 more sources

Braid lift representations of Artin's Braid Group

Journal of Knot Theory and Its Ramifications, 2000
We recast the braid-lift representation of Contantinescu, Lüdde and Toppan in the language of B-type braid theory. Composing with finite dimensional representations of these braid groups we obtain various sequences of finite dimensional multi-parameter representations.
openaire   +1 more source