classical braid group

GPTKB entity

Statements (48)
Predicate Object
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
https://www.w3.org/2000/01/rdf-schema#label 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}
gptkbp:notation B_n
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
gptkbp:bfsLayer 8