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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.

• 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 (H96E1)
• Jordan Algebras
  • JordanTripleProduct(J) : AlgGen -> TenSpcElt
  • JordanSpinAlgebra(F) : TenSpcElt -> AlgGen
  • Example AlgNAss_Ten_Jordan_Basic (H96E2)
  • ExceptionalJordanCSA(O) : AlgGen -> AlgGen
  • Example AlgNAss_Ten_Chevalley_Shafer_F4 (H96E3)
• Invariants
  • Center(A) : Alg -> Alg
  • Centroid(A) : Alg -> AlgMat
  • Example AlgNAss_CenterCentroids (H96E4)
  • LeftNucleus(A) : Alg -> AlgMat
  • DerivationAlgebra(A) : Alg -> AlgMatLie
  • Example AlgNAss_DerivationAlg (H96E5)
  • Example AlgNAss_Alg_Invariants (H96E6)
• Generic Operations
  • Nonassociative Algebras with Involutions
    • IsStarAlgebra(A) : AlgGen -> BoolElt
    • Star(A) : AlgGen -> Map
    • Example AlgNAss_Star_Alg (H96E7)
  • 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 (H96E8)
• Bibliography

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