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).