gptkbp:instanceOf
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gptkb:algebra
gptkb:group_of_people
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gptkbp:application
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gptkb:statistical_mechanics
gptkb:quantum_computing
cryptography
robotics
knot theory
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gptkbp:category
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gptkb:braid_theory
group theory
low-dimensional topology
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gptkbp:centralTo
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infinite cyclic group
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gptkbp:definedIn
|
n strands
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gptkbp:field
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gptkb:algebra
gptkb:mathematics
gptkb:topology
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gptkbp:generation
|
σ₁, σ₂, ..., σ_{n-1}
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gptkbp:hasSubgroup
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pure braid group
|
https://www.w3.org/2000/01/rdf-schema#label
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classical 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}
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gptkbp:notation
|
B_n
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gptkbp:presentedBy
|
gptkb:Artin_presentation
|
gptkbp:relatedTo
|
gptkb:Yang–Baxter_equation
gptkb:group_of_people
gptkb:Jones_polynomial
gptkb:Artin_group
gptkb:Burau_representation
gptkb:Hecke_algebra
mapping class group
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
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gptkbp:bfsLayer
|
8
|