Construction of Associative Algebras
Construction of an Associative Structure Constant Algebra
AssociativeAlgebra< R, n | Q : parameters > : Rng, RngIntElt, SeqEnum -> AlgAss
AssociativeAlgebra< R, n | T : parameters > : Rng, RngIntElt, SeqEnum -> AlgAss
AssociativeAlgebra(A) : AlgGen -> AlgAss
Associative Structure Constant Algebras from other Algebras
Algebra(A) : AlgGrp -> AlgAss, Map
Algebra(F, E) : FldFin, FldFin -> AlgAss, Map;
Operations on Associative Algebras and their Elements
Operations on Associative Algebras
Centre(A) : AlgAss -> AlgAss
Centralizer(A, S) : AlgAss, AlgAss -> AlgAss
Idealizer(A, B: parameters) : AlgAss, AlgAss -> AlgAss
LieAlgebra(A) : AlgAss -> AlgGen, Map
CommutatorModule(A, B) : AlgAss, AlgAss -> ModTupRng
CommutatorIdeal(A, B) : AlgAss, AlgAss -> AlgAss
LeftAnnihilator(A, B) : AlgAss, AlgAss -> AlgAss, AlgAss
RightAnnihilator(A, B) : AlgAss, AlgAss -> AlgAss, AlgAss
Example AlgAss_liealg (H69E1)
Operations on Elements
Centralizer(A, s) : AlgAss, AlgAssElt -> AlgAss
LieBracket(a, b) : AlgAssElt, AlgAssElt -> AlgAssElt
IsScalar(a) : AlgAssElt -> BoolElt, RngElt
RepresentationMatrix(a, M : parameters) : AlgAssElt, AlgAss -> AlgMatElt
Representations of Associative Algebras
MatrixAlgebra(A) : AlgAss -> AlgMat
MatrixAlgebra(A, M : parameters) : AlgAss, AlgAss -> AlgMat, Map
RegularRepresentation(A : parameters) : AlgAss -> AlgMat, Map
Decomposition of an Associative Algebra
JacobsonRadical(A) : AlgAssV -> AlgAssV
Example AlgAss_jac_rad (H69E2)
CentralIdempotents(A) : AlgAssV -> SeqEnum, SeqEnum