Definition:Lie Algebra

Definition
Let $\struct {A_R, \oplus}$ be an algebra over a ring.

Then $\struct {A_R, \oplus}$ is a Lie algebra :


 * $\forall a \in A_R: a^2 = 0$


 * $\forall a, b, c \in A_R: a \paren {b c} + b \paren {c a} + c \paren {a b} = 0$