Exercise 8, § 1 Lie Groups and Lie Algebras, I, 74 If x1,x2,x3,x4x_1, x_2, x_3, x_4x1,x2,x3,x4 are 4 elements of a Lie algebra, then [[[x1,x2],x3],x4]+[[[x2,x1],x4],x3]+[[[x3,x4],x1],x2]+[[[x4,x3],x2],x1]=0. [[[x_1, x_2], x_3], x_4] + [[[x_2, x_1], x_4], x_3] \\ + [[[x_3, x_4], x_1], x_2] + [[[x_4, x_3], x_2], x_1] = 0. [[[x1,x2],x3],x4]+[[[x2,x1],x4],x3]+[[[x3,x4],x1],x2]+[[[x4,x3],x2],x1]=0. Solution No solution has been written yet.