Lie Algebra

A Lie algebra $\mathfrak{g}$ over a Commutative Ring $R$ is an $R$-Module that is equipped with an Alternating, Bilinear Map that satisfies the Jacobi Identity.

Intuitively, a Lie Algebra encodes the Tangent Space of Lie Group at the identity element.

Questions

• Does this make sense for a general $(R,R)$-Bimodule? Bilinearity certainly does, as does the alternating property. Moreover, the Jacobi Identity seems to work just fine as well. Howe