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STRUCTURE CONSTANT ALGEBRAS

 
Acknowledgements
 
Introduction
 
Construction of Structure Constant Algebras and Elements
      Construction of a Structure Constant Algebra
      Construction of Elements of a Structure Constant Algebra
 
Operations on Structure Constant Algebras and Elements
      Operations on Structure Constant Algebras
      Indexing Elements
      The Module Structure of a Structure Constant Algebra
      Homomorphisms







DETAILS

 
Introduction

 
Construction of Structure Constant Algebras and Elements

      Construction of a Structure Constant Algebra
            Algebra< R, n | Q : parameters > : Rng, RngIntElt, SeqEnum -> AlgGen
            Algebra< R, n | T : parameters > : Rng, RngIntElt, SeqEnum -> AlgGen
            ChangeBasis(A, B) : AlgGen, [AlgGenElt] -> AlgGen

      Construction of Elements of a Structure Constant Algebra
            elt< A | r1, r2, ..., rn > : AlgGen, RngElt, RngElt, ..., RngElt -> AlgGenElt
            A ! Q : AlgGen, SeqEnum[RngElt] -> AlgGenElt
            BasisProduct(A, i, j) : AlgGen, RngIntElt, RngIntElt -> AlgGenElt
            BasisProducts(A) : AlgGen -> SeqEnum

 
Operations on Structure Constant Algebras and Elements

      Operations on Structure Constant Algebras
            IsCommutative(A) : AlgGen -> BoolElt
            IsAssociative(A) : AlgGen -> BoolElt
            IsLie(A) : AlgGen -> BoolElt
            DirectSum(A, B) : AlgGen, AlgGen -> AlgGen
            Example AlgCon_jordan (H80E1)

      Indexing Elements
            a[i] : AlgGenElt, RngIntElt -> RngElt
            a[i] := r : AlgGenElt, RngIntElt, RngElt -> AlgGenElt

      The Module Structure of a Structure Constant Algebra
            Module(A) : AlgGen -> ModTupRng
            Degree(A) : AlgGen -> RngIntElt
            Degree(a) : AlgGenElt -> RngIntElt
            ElementToSequence(a) : AlgGenElt -> SeqEnum
            Coordinates(S, a) : AlgGen, AlgGenElt -> SeqEnum
            InnerProduct(a, b) : AlgGenElt, AlgGenElt -> RngElt
            Support(a) : AlgGenElt -> SetEnum

      Homomorphisms
            hom< A -> B | Q > : AlgGen, AlgGen, [ AlgGenElt ] -> Map
            Example AlgCon_cayley (H80E2)

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