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ASSOCIATIVE ALGEBRAS

 
Acknowledgements
 
Introduction
 
Construction of Associative Algebras
      Construction of an Associative Structure Constant Algebra
      Associative Structure Constant Algebras from other Algebras
 
Operations on Associative Algebras and their Elements
      Operations on Associative Algebras
      Operations on Elements
      Representations of Associative Algebras
      Decomposition of an Associative Algebra
 
Bibliography







DETAILS

 
Introduction

 
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

 
Bibliography