A number of constructions for non-associative algebras are given in this chapter. The types of algebra currently available are constructed using the exceptional tensor machinery provided by the Multilinear Algebra package developed by Josh Maglione and James Wilson. A few supporting functions for nonassociative algebras are also provided.  
Acknowledgements
 
Composition Algebras
 
Jordan Algebras
 
Invariants
 
Generic Operations
      Nonassociative Algebras with Involutions
      Operations on Power Associative Algebras
 
Bibliography

 
Composition Algebras
      CompositionAlgebra(K, a) : Fld, [FldElt] -> AlgGen
      OctonionAlgebra(K, a, b, c) : Fld, FldElt, FldElt, FldElt -> AlgGen
      SplitOctonionAlgebra(K) : Fld -> AlgGen
      Example AlgNAss_Ten_Triality (H98E1)

 
Jordan Algebras
      JordanTripleProduct(J) : AlgGen -> TenSpcElt
      JordanSpinAlgebra(F) : TenSpcElt -> AlgGen
      Example AlgNAss_Ten_Jordan_Basic (H98E2)
      ExceptionalJordanCSA(O) : AlgGen -> AlgGen
      Example AlgNAss_Ten_Chevalley_Shafer_F4 (H98E3)

 
Invariants
      Center(A) : Alg -> Alg
      Centroid(A) : Alg -> AlgMat
      Example AlgNAss_CenterCentroids (H98E4)
      LeftNucleus(A) : Alg -> AlgMat
      DerivationAlgebra(A) : Alg -> AlgMatLie
      Example AlgNAss_DerivationAlg (H98E5)
      Example AlgNAss_Alg_Invariants (H98E6)

 
Generic Operations

      Nonassociative Algebras with Involutions
            IsStarAlgebra(A) : AlgGen -> BoolElt
            Star(A) : AlgGen -> Map
            Example AlgNAss_Star_Alg (H98E7)

      Operations on Power Associative Algebras
            GenericMinimalPolynomial(x) : AlgGenElt -> FldElt
            GenericNorm(x) : AlgGenElt -> FldElt
            GenericTrace(x) : AlgGenElt -> FldElt
            GenericTracelessSubspaceBasis(A) : AlgGen -> Any
            Example AlgNAss_Ten_Generic (H98E8)

 
Bibliography

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