Lie groups - IME-USP
... b. [[X, Y ], Z] + [[Y, Z], X] + [[Z, X], Y ] = 0 (Jacobi identity);
for every X, Y ∈ X(M ). In general, a vector space with a bilinear operation
satisfying (a) and (b) above is called a Lie algebra. So X(M ) is Lie algebra
It turns out in case of a Lie group G, we can single out a finite dim ...