Lie Ring

A Lie ring is defined as a nonassociative ring with multiplication that is anticommutative and satisfies the Jacobi identity. More specifically we can define a Lie ring to be an abelian group with an operation that has the following properties:

• Bilinearity:

for all x, y, z ∈ L.

• The Jacobi identity:

for all x, y, z in L.

• For all x in L.