|
gptkbp:instanceOf
|
gptkb:algebra
gptkb:group_of_people
|
|
gptkbp:application
|
gptkb:statistical_mechanics
gptkb:quantum_computing
cryptography
robotics
knot theory
|
|
gptkbp:category
|
gptkb:braid_theory
group theory
low-dimensional topology
|
|
gptkbp:centralTo
|
infinite cyclic group
|
|
gptkbp:definedIn
|
n strands
|
|
gptkbp:field
|
gptkb:algebra
gptkb:mathematics
gptkb:topology
|
|
gptkbp:generation
|
σ₁, σ₂, ..., σ_{n-1}
|
|
gptkbp:hasSubgroup
|
pure braid group
|
|
gptkbp:introduced
|
gptkb:Emil_Artin
|
|
gptkbp:introducedIn
|
1925
|
|
gptkbp:isFinite
|
true
|
|
gptkbp:isFinitelyGenerated
|
true
|
|
gptkbp:isFinitelyPresented
|
true
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isomorphicTo
|
mapping class group of n-punctured disk
|
|
gptkbp:isQuotientOf
|
gptkb:group_of_people
|
|
gptkbp:loveInterest
|
σ_i σ_j = σ_j σ_i for |i-j|>1
σ_i σ_{i+1} σ_i = σ_{i+1} σ_i σ_{i+1}
|
|
gptkbp:notation
|
B_n
|
|
gptkbp:presentedBy
|
gptkb:Artin_presentation
|
|
gptkbp:relatedTo
|
gptkb:Yang–Baxter_equation
gptkb:group_of_people
gptkb:mapping_class_group
gptkb:Jones_polynomial
gptkb:Artin_group
gptkb:Burau_representation
gptkb:Hecke_algebra
braid monoid
configuration space
Markov moves
Garside structure
braid closure
loop braid group
virtual braid group
braid word
braid diagram
|
|
gptkbp:bfsParent
|
gptkb:surface_braid_group
|
|
gptkbp:bfsLayer
|
8
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
classical braid group
|