# Non–Associative Algebras

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](Composition-algebras.md)

  - [`CompositionAlgebra(K, a): Fld, [FldElt] → AlgGen`](Composition-algebras.md#function-compositionalgebra-fld-fldelt)

  - [`CompositionAlgebra(K, a): Fld, [RngIntElt] → AlgGen`](Composition-algebras.md#function-compositionalgebra-fld-rngintelt)

  - [`OctonionAlgebra(K, a, b, c): Fld, FldElt, FldElt, FldElt → AlgGen`](Composition-algebras.md#function-octonionalgebra-fld-fldelt-fldelt-fldelt)

  - [`OctonionAlgebra(K, a, b, c): Fld, RngIntElt, RngIntElt, RngIntElt → AlgGen`](Composition-algebras.md#function-octonionalgebra-fld-rngintelt-rngintelt-rngintelt)

  - [`SplitOctonionAlgebra(K): Fld → AlgGen`](Composition-algebras.md#function-splitoctonionalgebra-fld)

  - [`Example: Ten Triality`](Composition-algebras.md#example-ex-7d5c5a)

- [Jordan Algebras](Jordan-algebras.md)

  - [`JordanTripleProduct(J): AlgGen → TenSpcElt`](Jordan-algebras.md#function-jordantripleproduct-alggen)

  - [`JordanSpinAlgebra(F): TenSpcElt → AlgGen`](Jordan-algebras.md#function-jordanspinalgebra-tenspcelt)

  - [`JordanSpinAlgebra(F): Any → AlgGen`](Jordan-algebras.md#function-jordanspinalgebra-any)

  - [`Example: Ten Jordan Basic`](Jordan-algebras.md#example-ex-359672)

  - [`ExceptionalJordanCSA(O): AlgGen → AlgGen`](Jordan-algebras.md#function-exceptionaljordancsa-alggen)

  - [`ExceptionalJordanCSA(K): Fld → AlgGen`](Jordan-algebras.md#function-exceptionaljordancsa-fld)

  - [`Example: Ten Chevalley Shafer F4`](Jordan-algebras.md#example-ex-af7b0b)

- [Invariants](Invariants-of-nonassociative-algebras.md)

  - [`Center(A): Alg → Alg`](Invariants-of-nonassociative-algebras.md#function-center-alg)

  - [`Centre(A): Alg → Alg`](Invariants-of-nonassociative-algebras.md#function-centre-alg)

  - [`Centroid(A): Alg → AlgMat`](Invariants-of-nonassociative-algebras.md#function-centroid-alg)

  - [`Example: Center Centroids`](Invariants-of-nonassociative-algebras.md#example-ex-ebe4ae)

  - [`LeftNucleus(A): Alg → AlgMat`](Invariants-of-nonassociative-algebras.md#function-leftnucleus-alg)

  - [`RightNucleus(A): Alg → AlgMat`](Invariants-of-nonassociative-algebras.md#function-rightnucleus-alg)

  - [`MidNucleus(A): Alg → AlgMat`](Invariants-of-nonassociative-algebras.md#function-midnucleus-alg)

  - [`DerivationAlgebra(A): Alg → AlgMatLie`](Invariants-of-nonassociative-algebras.md#function-derivationalgebra-alg)

  - [`Example: Derivation Alg`](Invariants-of-nonassociative-algebras.md#example-ex-8c0a5c)

  - [`Example: Alg Invariants`](Invariants-of-nonassociative-algebras.md#example-ex-a850f6)

- [Generic Operations](Generics-for-nonassociative-algebras.md)

  - [Nonassociative Algebras with Involutions](Generics-for-nonassociative-algebras.md#nonassociative-algebras-with-involutions)

    - [`IsStarAlgebra(A): AlgGen → BoolElt`](Generics-for-nonassociative-algebras.md#function-isstaralgebra-alggen)

    - [`Star(A): AlgGen → Map`](Generics-for-nonassociative-algebras.md#function-star-alggen)

    - [`Example: Star Alg`](Generics-for-nonassociative-algebras.md#example-ex-ffb750)

  - [Operations on Power Associative Algebras](Generics-for-nonassociative-algebras.md#operations-on-power-associative-algebras)

    - [`GenericMinimalPolynomial(x): AlgGenElt → FldElt`](Generics-for-nonassociative-algebras.md#function-genericminimalpolynomial-alggenelt)

    - [`GenericNorm(x): AlgGenElt → FldElt`](Generics-for-nonassociative-algebras.md#function-genericnorm-alggenelt)

    - [`GenericTrace(x): AlgGenElt → FldElt`](Generics-for-nonassociative-algebras.md#function-generictrace-alggenelt)

    - [`GenericTracelessSubspaceBasis(A): AlgGen → Any`](Generics-for-nonassociative-algebras.md#function-generictracelesssubspacebasis-alggen)

    - [`Example: Ten Generic`](Generics-for-nonassociative-algebras.md#example-ex-099024)