Lie-admissible algebra

Summary

A Lie-admissible algebra is a nonassociative algebra whose commutator $xy - yx$ is a Lie bracket. Thus every Lie-admissible algebra $A$ gives a Lie algebra $A^-$ on the same vector space. Associative algebras and pre-Lie algebras are Lie-admissible. The notion singles out those algebras whose commutator is a Lie bracket, as it is for an associative algebra.