Solvable Lie algebra application


I am starting to study Lie algebras and when I reached the notion of solvable Lie algebra, I tryed to find concrete applications ( in physics for exemple) and I couldn’t find one. Solvable group are very important for the unsolvability of quintic equation ( and by the way, it’s the only application I know of them).

In the same manner, can we find application for solvable lie algebras ?