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 (H96E1)

      Basic Attributes of *-Algebras
            IsStarAlgebra(A) : AlgMat -> BoolElt
            Star(A) : AlgMat -> Map

      Adjoint Algebras
            AdjointAlgebra(S : parameters) : SeqEnum -> AlgMat
            Example AlgInv_AdjointAlgebra (H96E2)

      Group Algebras
            StarOnGroupAlgebra(A) : AlgGrp -> Map
            GroupAlgebraAsStarAlgebra(R, G) : Rng, Grp -> AlgGrp
            Example AlgInv_GroupAlgebraAsStarAlgebra (H96E3)
            Example AlgInv_GroupAlgebraAsStarAlgebra2 (H96E4)

      Simple *-Algebras
            SimpleStarAlgebra(name, d, K) : MonStgElt, RngIntElt, FldFin -> AlgMat
            Example AlgInv_SimpleStarAlgebra (H96E5)

 
Decompositions of *-Algebras
      WedderburnDecomposition(A) : AlgMat -> AlgMat, AlgMat
      TaftDecomposition(A) : AlgMat -> AlgMat, AlgMat
      Example AlgInv_TaftDcomposition (H96E6)

 
Recognition of *-Algebras

      Recognition of Simple *-Algebras
            RecogniseClassicalSSA(A) : AlgMat -> BoolElt, AlgMat, Map, Map
            RecogniseExchangeSSA(A) : AlgMat -> BoolElt, AlgMat, Map, Map
            Example AlgInv_RecogniseClassicalSSA (H96E7)

      Recognition of Arbitrary *-Algebras
            RecogniseStarAlgebra(A) : AlgMat -> BoolElt
            IsSimpleStarAlgebra(A) : AlgMat -> BoolElt
            SimpleParameters(A) : AlgMat -> SeqEnum
            NormGroup(A) : AlgMat -> GrpMat
            Example AlgInv_Nonisomorphism1 (H96E8)
            Example AlgInv_Nonisomorphism2 (H96E9)

 
Intersections of Classical Groups
      IsometryGroup(S : parameters) : SeqEnum -> GrpMat
      Example AlgInv_IsometryGroup (H96E10)
      ClassicalIntersection(S) : SeqEnum -> GrpMat
      Example AlgInv_ClassicalIntersection (H96E11)

 
Bibliography

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