  We show that every finite non-degenerate set theoretical solution to the YBE
whose retraction is a flip linearizes to a twist of the flip solution by roots
of unity. This generalizes a result of Gateva-Ivanova and Majid. To prove the
result we use a new invariant associated to a solution, its Lie algebra. We
show also that a solution retracts to a flip solution if and only if its Lie
algebra is abelian.
