Construction of Group Algebras and their Elements
Construction of a Group Algebra
GroupAlgebra( R, G: parameters ) : Rng, Grp -> AlgGrp
Example AlgGrp_creation (H84E1)
Construction of a Group Algebra Element
elt< A | r, g > : AlgGrp, RngElt, GrpElt -> AlgGrpElt
A ! g : AlgGrp, GrpElt -> AlgGrpElt
A ! r : AlgGrp, RngElt -> AlgGrpElt
A ! [c1, ..., cn] : AlgGrp, SeqEnum -> AlgGrpElt
Eta(A) : AlgGrp -> AlgGrpElt
Example AlgGrp_el-creation (H84E2)
Construction of Subalgebras, Ideals and Quotient Algebras
sub< cat : A | L> : Cat, AlgGrp, List -> AlgGrp, Map
lideal< cat : A | L> : Cat, AlgGrp, List -> AlgGrp, Map
rideal< cat : A | L> : Cat, AlgGrp, List -> AlgGrp, Map
ideal< cat : A | L> : Cat, AlgGrp, List -> AlgGrp, Map
a * I : AlgGrpElt, AlgGrpSub -> AlgGrpSub
I * a : AlgGrpSub, AlgGrpElt -> AlgGrpSub
quo< A | L > : AlgGrp, List -> AlgAss, Map
A / S : AlgGrp, AlgGrpSub -> AlgAss
Example AlgGrp_wedderburn (H84E3)
Operations on Group Algebras and their Subalgebras
Operations on Group Algebras
Algebra(A) : AlgGrp -> AlgAss, Map
AugmentationMap(A) : AlgGrp -> Map
AugmentationIdeal(A) : AlgGrp -> AlgGrpSub
RepresentationType(A) : AlgGrp -> MonStgElt
ChangeRepresentationType(A, Rep) : AlgGrp, MonStgElt -> AlgGrp, Map
ConstructTable(A) : AlgGrp ->
CoefficientRing(A) : AlgGrp -> Rng
Operations on Subalgebras of Group Algebras
S ! 1 : AlgGrpSub -> Grp
Group(S) : AlgGrpSub -> Grp
GroupAlgebra(S) : AlgGrpSub -> AlgGrp
Module(S) : AlgGrpSub -> ModTupRng, Map
CoefficientRing(A) : AlgGrpSub -> Rng
BasisMatrix(S) : AlgGrpSub -> ModMatRngElt
Coordinates(S, a) : AlgGrpSub, AlgGrpElt -> [ RingElt ]
IsLeftIdeal(S) : AlgGrpSub -> BoolElt
IsRightIdeal(S) : AlgGrpSub -> BoolElt
IsIdeal(S) : AlgGrpSub -> BoolElt
Centraliser(S) : AlgGrpSub -> AlgGrpSub
Idealiser(S) : AlgGrpSub -> AlgGrpSub
LeftAnnihilator(S) : AlgGrpSub -> AlgGrpSub
RightAnnihilator(S) : AlgGrpSub -> AlgGrpSub
Example AlgGrp_jacobson (H84E4)
Operations on Elements
a + r : AlgGrpElt, RngElt -> AlgGrpElt
a + g : AlgGrpElt, GrpElt -> AlgGrpElt
a - r : AlgGrpElt, RngElt -> AlgGrpElt
a - g : AlgGrpElt, GrpElt -> AlgGrpElt
a * r : AlgGrpElt, RngElt -> AlgGrpElt
g * a : GrpElt, AlgGrpElt -> AlgGrpElt
Support(a) : AlgGrpElt -> SeqEnum
Trace(a) : AlgGrpElt -> RngElt
Augmentation(a) : AlgGrpElt -> RngElt
Involution(a) : AlgGrpElt -> AlgGrpElt
Coefficient(a, g) : AlgGrpElt, GrpElt -> RngElt
ElementToSequence(a) : AlgGrpElt -> SeqEnum
Coefficients(a) : AlgGrpElt -> SeqEnum
Centraliser(a) : AlgGrpElt -> AlgGrpSub
Centraliser(S, a) : AlgGrpSub, AlgGrpElt -> AlgGrpSub
Example AlgGrp_powering (H84E5)
Example AlgGrp_average (H84E6)
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Version: V2.19 of
Mon Dec 17 14:40:36 EST 2012