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Magma
Computer • algebra
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Introduction
Algebras with Involution
Reflexive Forms
IsometryGroup(F : parameters) : AlgMatElt -> GrpMat
SimilarityGroup(F : parameters) : AlgMatElt -> GrpMat
Systems of Reflexive Forms
PGroupToForms(G) : GrpPC -> SeqEnum
PGroupToForms(G) : GrpMat -> SeqEnum
Example
AlgInv_PGroupToForms (H94E1)
Basic Attributes of *-Algebras
IsStarAlgebra(A) : AlgMat -> BoolElt
Star(A) : AlgMat -> Map
Adjoint Algebras
AdjointAlgebra(S : parameters) : SeqEnum -> AlgMat
Example
AlgInv_AdjointAlgebra (H94E2)
Group Algebras
StarOnGroupAlgebra(A) : AlgGrp -> Map
GroupAlgebraAsStarAlgebra(R, G) : Rng, Grp -> AlgGrp
Example
AlgInv_GroupAlgebraAsStarAlgebra (H94E3)
Example
AlgInv_GroupAlgebraAsStarAlgebra2 (H94E4)
Simple *-Algebras
SimpleStarAlgebra(name, d, K) : MonStgElt, RngIntElt, FldFin -> AlgMat
Example
AlgInv_SimpleStarAlgebra (H94E5)
Decompositions of *-Algebras
WedderburnDecomposition(A) : AlgMat -> AlgMat, AlgMat
TaftDecomposition(A) : AlgMat -> AlgMat, AlgMat
Example
AlgInv_TaftDcomposition (H94E6)
Recognition of *-Algebras
Recognition of Simple *-Algebras
RecogniseClassicalSSA(A) : AlgMat -> BoolElt, AlgMat, Map, Map
RecogniseExchangeSSA(A) : AlgMat -> BoolElt, AlgMat, Map, Map
Example
AlgInv_RecogniseClassicalSSA (H94E7)
Recognition of Arbitrary *-Algebras
RecogniseStarAlgebra(A) : AlgMat -> BoolElt
IsSimpleStarAlgebra(A) : AlgMat -> BoolElt
SimpleParameters(A) : AlgMat -> SeqEnum
NormGroup(A) : AlgMat -> GrpMat
Example
AlgInv_Nonisomorphism1 (H94E8)
Example
AlgInv_Nonisomorphism2 (H94E9)
Intersections of Classical Groups
IsometryGroup(S : parameters) : SeqEnum -> GrpMat
Example
AlgInv_IsometryGroup (H94E10)
ClassicalIntersection(S) : SeqEnum -> GrpMat
Example
AlgInv_ClassicalIntersection (H94E11)
Bibliography
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V2.28, 13 July 2023