A vector space V together with a Lie bracket, a map V×V →V denoted by [x,y] where x,y ∈ V, which is bilinear, alternating so that [x,x] = 0 for all x, and which satisfies Jacobi’s identity. One example is V = ℝ3 with the Lie bracket being the vector product. For any Lie group, the tangent space at the identity element is a Lie algebra. The Lie algebra of a Lie group G is often denoted in gothic as 𝔤.