|
gptkbp:instanceOf
|
gptkb:algebra
gptkb:group_of_people
|
|
gptkbp:application
|
gptkb:topology
gptkb:quantum_computing
cryptography
knot theory
|
|
gptkbp:category
|
gptkb:Artin_group
|
|
gptkbp:centralTo
|
infinite cyclic group
|
|
gptkbp:containsElement
|
braid
|
|
gptkbp:definedIn
|
gptkb:Artin_presentation
|
|
gptkbp:dependsOn
|
number of strands n
|
|
gptkbp:firstDefined
|
1925
|
|
gptkbp:generation
|
sigma_1
sigma_2
sigma_{n-1}
|
|
gptkbp:hasConjugacyProblem
|
solvable
|
|
gptkbp:hasSpecialCase
|
B_1 is trivial group
B_2 is infinite cyclic group
|
|
gptkbp:hasSubgroup
|
automorphism group of free group
|
|
gptkbp:hasWordProblem
|
solvable
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
braid group B n
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isQuotientOf
|
mapping class group of n-punctured disk
|
|
gptkbp:loveInterest
|
sigma_i sigma_j = sigma_j sigma_i for |i-j|>1
sigma_i sigma_{i+1} sigma_i = sigma_{i+1} sigma_i sigma_{i+1}
|
|
gptkbp:namedAfter
|
gptkb:Emil_Artin
|
|
gptkbp:operator
|
concatenation of braids
|
|
gptkbp:order
|
infinite
|
|
gptkbp:relatedTo
|
gptkb:quantum_field_theory
gptkb:symmetric_group_S_n
gptkb:Jones_polynomial
gptkb:Hecke_algebra
gptkb:modular_tensor_category
mapping class group
braid monoid
braid relations
pure braid group
knot invariants
Markov moves
Garside structure
braid closure
configuration space of n points in the plane
loop braid group
mapping class group of the disk with n punctures
virtual braid group
|
|
gptkbp:represents
|
gptkb:Burau_representation
gptkb:Lawrence–Krammer_representation
|
|
gptkbp:usedIn
|
gptkb:Yang–Baxter_equation
|
|
gptkbp:bfsParent
|
gptkb:Burau_representation
|
|
gptkbp:bfsLayer
|
7
|