Introduction
Construction of Group Algebras and their Elements
Construction of a Group Algebra GroupAlgebra( R, G: parameters ) : Rng, Grp -> AlgGrp Example AlgGrp_creation (H88E1)
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 (H88E2)
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 (H88E3)
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 ->
Operations on Subalgebras of Group Algebras S ! 1 : AlgGrpSub -> Grp Group(S) : AlgGrpSub -> Grp GroupAlgebra(S) : AlgGrpSub -> AlgGrp Module(S) : AlgGrpSub -> ModTupRng, Map 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 (H88E4)
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 (H88E5) Example AlgGrp_average (H88E6) [Next][Prev] [Right] [____] [Up] [Index] [Root]
