Statements (29)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:alsoKnownAs |
gptkb:Artin_group
|
| gptkbp:definedIn |
gptkb:Weyl_group
gptkb:Coxeter_matrix presentation with generators and relations |
| gptkbp:generalizes |
braid group
|
| gptkbp:hasApplication |
gptkb:topology
combinatorics knot theory |
| gptkbp:hasProperty |
linear (in some cases)
residually finite (in some cases) torsion-free (in some cases) |
| gptkbp:hasSubgroup |
braid group
|
| gptkbp:hasType |
gptkb:affine_Artin_group
gptkb:right-angled_Artin_group gptkb:spherical_Artin_group |
| https://www.w3.org/2000/01/rdf-schema#label |
Artin–Tits group
|
| gptkbp:introducedIn |
20th century
|
| gptkbp:namedAfter |
gptkb:Emil_Artin
gptkb:Jacques_Tits |
| gptkbp:numberOfIssues |
word problem
center problem conjugacy problem |
| gptkbp:presentedBy |
generators a_i, relations of the form (a_i a_j)^{m_{ij}} = (a_j a_i)^{m_{ij}}
|
| gptkbp:relatedTo |
gptkb:Weyl_group
Artin relations |
| gptkbp:studiedIn |
geometric group theory
|
| gptkbp:bfsParent |
gptkb:Artin_group
|
| gptkbp:bfsLayer |
6
|