Admissible algebra

For a (possibly non-associative) algebra such that the product ab – ba or ab + ba satisfies a certain identity, see Jordan-admissible algebra, Lie-admissible algebra, and Malcev-admissible algebra.

In mathematics, an admissible algebra is a (possibly non-associative) commutative algebra whose enveloping Lie algebra of derivations splits into the sum of an even and an odd part. Admissible algebras were introduced by Koecher (1967).

References

• Koecher, Max (1967), "Imbedding of Jordan algebras into Lie algebras. I", Amer. J. Math., 89: 787–816, doi:10.2307/2373242, JSTOR 2373242, MR 0214631