|
gptkbp:instanceOf
|
gptkb:group_of_people
|
|
gptkbp:application
|
gptkb:algebraic_geometry
gptkb:statistical_mechanics
gptkb:quantum_computing
cryptography
robotics
|
|
gptkbp:category
|
gptkb:topology
group theory
combinatorial group theory
low-dimensional topology
|
|
gptkbp:centralTo
|
infinite cyclic group
|
|
gptkbp:containsElement
|
braid
|
|
gptkbp:definedIn
|
generators and relations
|
|
gptkbp:field
|
gptkb:mathematics
|
|
gptkbp:generalizes
|
gptkb:group_of_people
|
|
gptkbp:hasConjugacyProblem
|
solvable
|
|
gptkbp:hasFaithfulRepresentation
|
gptkb:Burau_representation
gptkb:Lawrence–Krammer_representation
|
|
gptkbp:hasSubfield
|
gptkb:algebra
gptkb:topology
|
|
gptkbp:hasWordProblem
|
solvable
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Artin braid group
|
|
gptkbp:introducedIn
|
1925
|
|
gptkbp:isAutomaticGroup
|
true
|
|
gptkbp:isFinitelyPresented
|
true
|
|
gptkbp:isGarsideGroup
|
true
|
|
gptkbp:isHopfian
|
true
|
|
gptkbp:isMatrixGroup
|
true
|
|
gptkbp:isResiduallyFinite
|
true
|
|
gptkbp:isTorsionFree
|
true
|
|
gptkbp:namedAfter
|
gptkb:Emil_Artin
|
|
gptkbp:notation
|
B_n
|
|
gptkbp:order
|
infinite
|
|
gptkbp:presentedBy
|
generators σ₁, σ₂, ..., σ_{n-1}
|
|
gptkbp:relatedTo
|
gptkb:Yang–Baxter_equation
gptkb:Jones_polynomial
gptkb:Hecke_algebra
gptkb:Vassiliev_invariants
gptkb:braid_theory
gptkb:mapping_class_group_of_punctured_disk
knot theory
quantum groups
mapping class group
braid monoid
configuration space
mapping class group of surfaces
pure braid group
|
|
gptkbp:satisfiesRelation
|
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:type
|
non-abelian
|
|
gptkbp:bfsParent
|
gptkb:Emil_Artin
|
|
gptkbp:bfsLayer
|
5
|