GroupBasis

A basis element of the group algebra , named by its group element's label. The product is the group's own multiplication, extended bilinearly.

WikipediaGroup ring↗MathWorldGroupRing↗WikidataQ2602722↗

GroupBasis(label)the basis element for that group element

GroupProduct(group, a, b)multiply — the group is named, since a basis element does not carry it

Domain: Group algebras

Details

• Groups: `CyclicGroup(n)` with elements , `DihedralGroup(n)` with elements `k` for and `s k` for , and `GroupDirectProduct(g, h)`
• multiplies by adding indices mod — it is
• is commutative exactly when is abelian
• Dihedral relations: , ,
• , and `Basis(GroupAlgebra(group))` lists the elements

Examples

See also: ClassSum, ConjugacyClasses, Basis