  The PostLie algebra is an enriched structure of the Lie algebra that has
recently arisen from operadic study. It is closely related to pre-Lie algebra,
Rota-Baxter algebra, dendriform trialgebra, modified classical Yang-Baxter
equations and integrable systems. We give a complete classification of PostLie
algebra structures on the Lie algebra sl(2,C) up to isomorphism. We first
reduce the classification problem to solving an equation of 3 x 3 matrices. To
solve the latter problem, we make use of the classification of complex
symmetric matrices up to the congruent action of orthogonal groups.
