Properties (63)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
musical group
|
| gptkbp:associatedWith |
Knot Theory
σ_iσ_j = σ_jσ_i for |i - j| > 1. |
| gptkbp:field |
Infinite dimensional.
|
| gptkbp:hasActivities |
With certain mapping class groups.
|
| gptkbp:hasClient |
To algebraic structures.
To algebraic topology. To category theory. To representation theory. |
| gptkbp:hasDepartment |
A group whose elements are braids and whose group operation is the concatenation of braids.
|
| gptkbp:hasGenre |
Braids with a finite number of strands.
|
| gptkbp:hasHistoricalSignificance |
Important in the development of modern algebra.
Introduced_by_Emil_Artin_in_1925. Studied_by_Emil_Artin. |
| gptkbp:hasHistory |
To the symmetric group.
|
| gptkbp:hasPerformedAt |
As a group of automorphisms.
|
| gptkbp:hasRelatedPatent |
Cryptography
Robotics. DNA topology. In combinatorial topology. In physics. In theoretical computer science. |
| gptkbp:hasSpecialty |
Associative.
Non-commutative. Closure, associativity, identity, and invertibility. |
| gptkbp:hasSubsidiary |
Artin_Braid_Group
|
| gptkbp:hasVariants |
Pure braid group.
|
| https://www.w3.org/2000/01/rdf-schema#label |
Braid Group
|
| gptkbp:isAssociatedWith |
Braided categories.
|
| gptkbp:isCharacterizedBy |
The braid group on n strands.
The braid group relations. The braid relations. |
| gptkbp:isCitedBy |
A set of generators and relations.
Generators and relations. |
| gptkbp:isConnectedTo |
The fundamental group of the configuration space.
Algebraic_Geometry. |
| gptkbp:isMaintainedBy |
Elementary braids.
|
| gptkbp:isMarriedTo |
True
|
| gptkbp:isRelatedTo |
Topology
Geometric group theory. Homological algebra. Homotopy theory. The study of knots. The theory of braids. |
| gptkbp:isRepresentedIn |
Braids in 3-dimensional space.
Braids on n strands. |
| gptkbp:isStudiedIn |
Mathematics.
Topology. Mathematical physics. Mathematical logic. Algebraic_Topology Theoretical_Physics. |
| gptkbp:isUsedIn |
gptkb:Quantum_Computing
Cryptographic protocols. String theory. The study of 3-manifolds. Topological quantum field theory. Computer_Graphics. Quantum_field_theory. |
| gptkbp:isUtilizedFor |
Small numbers of strands.
|
| gptkbp:isValuedFor |
A finite number of strands.
A finite set of strands. A set of strands. |