Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
|
| gptkbp:basisFor |
elements of G
|
| gptkbp:builtBy |
group G
field F |
| gptkbp:centralTo |
class functions on G
|
| gptkbp:containsElement |
formal sum \\sum a_g g with a_g in F, g in G
|
| gptkbp:definedIn |
gptkb:Field
|
| gptkbp:dimensions |
order of G
|
| gptkbp:hasSpecialCase |
group ring if F is a ring
|
| https://www.w3.org/2000/01/rdf-schema#label |
group algebra of G
|
| gptkbp:identityElement |
true
|
| gptkbp:if_F=\\mathbb{C}_and_G_finite, |
semisimple by Maschke's theorem
|
| gptkbp:if_G_finite_and_F_characteristic_does_not_divide_|G|, |
semisimple
|
| gptkbp:isAssociative |
true
|
| gptkbp:multiplication |
linear extension of group multiplication
|
| gptkbp:notation |
F[G]
|
| gptkbp:relatedTo |
character theory
group representation |
| gptkbp:usedIn |
representation theory
homological algebra module theory |
| gptkbp:bfsParent |
gptkb:L^1_group_algebra
|
| gptkbp:bfsLayer |
6
|