Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
set with group action |
| gptkbp:category |
category of G-sets
|
| gptkbp:definedIn |
set X with a group G acting on it
|
| gptkbp:example |
group G acting on a coset space G/H
group G acting on itself by left multiplication group G acting trivially on a set |
| gptkbp:field |
abstract algebra
|
| gptkbp:hasProperty |
for all g,h in G and x in X, g·(h·x) = (gh)·x
for all x in X, e·x = x where e is the identity in G |
| https://www.w3.org/2000/01/rdf-schema#label |
G-set
|
| gptkbp:morphism |
G-equivariant map
|
| gptkbp:notation |
(X, G)
G \\curvearrowright X |
| gptkbp:relatedConcept |
gptkb:Titan
gptkb:Burnside's_lemma homogeneous space stabilizer permutation representation fixed point free action faithful action transitive G-set |
| gptkbp:structure |
set with a map G × X → X
functor from group G (as a one-object category) to Set |
| gptkbp:studiedBy |
gptkb:Évariste_Galois
|
| gptkbp:used_in |
gptkb:topology
gptkb:category_theory group theory representation theory |
| gptkbp:bfsParent |
gptkb:G-spaces
|
| gptkbp:bfsLayer |
7
|