Exercise 7, § 5

Let $g$ be the 3-dimensional solvable Lie algebra with basis $(x, y, z)$ such that $[x, y] = z,\ [x, z] = y,\ [y, z] = 0$. Show that the linear mapping which maps $x$ to $-x,\ y$ to $-z,\ z$ to $y$ is an automorphism of $g$ of order 4. Compare this result with Exercise 21 (c) of § 4.