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
CompositionAlgebra(K, a): Fld, [FldElt] → AlgGenCompositionAlgebra(K, a): Fld, [RngIntElt] → AlgGenOctonionAlgebra(K, a, b, c): Fld, FldElt, FldElt, FldElt → AlgGenOctonionAlgebra(K, a, b, c): Fld, RngIntElt, RngIntElt, RngIntElt → AlgGenSplitOctonionAlgebra(K): Fld → AlgGen- Example: Triality in Octonion Algebras
- Jordan Algebras
- Invariants
Center(A): Alg → AlgCentre(A): Alg → AlgCentroid(A): Alg → AlgMat- Example: Center and Centroid of an Algebra
LeftNucleus(A): Alg → AlgMatRightNucleus(A): Alg → AlgMatMidNucleus(A): Alg → AlgMatDerivationAlgebra(A): Alg → AlgMatLie- Example: Derivation Algebra of the Octonions
- Example: Further Invariants of Nonassociative Algebras
- Generic Operations
- Bibliography