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ALGEBRAS WITH INVOLUTION

 
Acknowledgements
 
Introduction
 
Algebras with Involution
      Reflexive Forms
      Systems of Reflexive Forms
      Basic Attributes of *-Algebras
      Adjoint Algebras
      Group Algebras
      Simple *-Algebras
 
Decompositions of *-Algebras
 
Recognition of *-Algebras
      Recognition of Simple *-Algebras
      Recognition of Arbitrary *-Algebras
 
Intersections of Classical Groups
 
Bibliography







DETAILS

 
Introduction

 
Algebras with Involution

      Reflexive Forms
            IsometryGroup(F : parameters) : AlgMatElt -> GrpMat
            SimilarityGroup(F : parameters) : AlgMatElt -> GrpMat

      Systems of Reflexive Forms
            PGroupToForms(G) : GrpPC -> SeqEnum
            Example AlgInv_PGroupToForms (H87E1)

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

      Adjoint Algebras
            AdjointAlgebra(S : parameters) : SeqEnum -> AlgMat
            Example AlgInv_AdjointAlgebra (H87E2)

      Group Algebras
            StarOnGroupAlgebra(A) : AlgGrp -> Map
            GroupAlgebraAsStarAlgebra(R, G) : Rng, Grp -> AlgGrp
            Example AlgInv_GroupAlgebraAsStarAlgebra (H87E3)

      Simple *-Algebras
            SimpleStarAlgebra(name, d, K) : MonStgElt, RngIntElt, FldFin -> AlgMat
            Example AlgInv_SimpleStarAlgebra (H87E4)

 
Decompositions of *-Algebras
      WedderburnDecomposition(A) : AlgMat -> AlgMat, AlgMat
      TaftDecomposition(A) : AlgMat -> AlgMat, AlgMat
      Example AlgInv_TaftDcomposition (H87E5)

 
Recognition of *-Algebras

      Recognition of Simple *-Algebras
            RecogniseClassicalSSA(A) : AlgMat -> BoolElt, AlgMat, Map, Map
            RecogniseExchangeSSA(A) : AlgMat -> BoolElt, AlgMat, Map, Map
            Example AlgInv_RecogniseClassicalSSA (H87E6)

      Recognition of Arbitrary *-Algebras
            RecogniseStarAlgebra(A) : AlgMat -> BoolElt
            IsSimpleStarAlgebra(A) : AlgMat -> BoolElt
            SimpleParameters(A) : AlgMat -> SeqEnum
            NormGroup(A) : AlgMat -> GrpMat
            Example AlgInv_Nonisomorphism1 (H87E7)
            Example AlgInv_Nonisomorphism2 (H87E8)

 
Intersections of Classical Groups
      IsometryGroup(S : parameters) : SeqEnum -> GrpMat
      Example AlgInv_IsometryGroup (H87E9)
      ClassicalIntersection(S) : SeqEnum -> GrpMat
      Example AlgInv_ClassicalIntersection (H87E10)

 
Bibliography

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Version: V2.19 of Wed Apr 24 15:09:57 EST 2013