I read in Karin Erdmann and Mark J. Wildon's book "introduction to lie algebras" "Let F be any field. Up to isomorphism there is a unique two-dimensional nonabelian Lie algebra over F. This Lie algebra has a basis {x, y} such that its Lie bracket is described by [x, y] = x"
How can i proof this bracket [x,y] = x satisfies axioms of Lie algebra such that [a,a] = 0 for $a \in L$ and satisfies jacoby identity
and can some one give me an example of two dimensional nonabelian Lie algebra