  A non-abelian phase space, or a phase space of a Lie algebra is a
generalization of the usual (abelian) phase space of a vector space. It
corresponds to a parak\"ahler structure in geometry. Its structure can be
interpreted in terms of left-symmetric algebras. In particular, a solution of
an algebraic equation in a left-symmetric algebra which is an analogue of
classical Yang-Baxter equation in a Lie algebra can induce a phase space. In
this paper, we find that such phase spaces have a symplectically isomorphic
property. We also give all such phase spaces in dimension 4 and some examples
in dimension 6. These examples can be a guide for a further development.
