Quasi-Lie algebras and a method for determining non-degeneracy of the quasi-Lie product

The axioms of a quasi-lie algebra are stated, followed by the definition of a nondegenerate quasi-lie algebra which is given in the framework of HopF algebra theory. Some quantum Lie algebras are shown to be examples of non-degenerate quasi-lie algebras and a method of testing for this non-degeneracy is outlined. It is shown that non-degeneracy implies uniqueness of the symmetriser. For quantum Lie algebras this is surprising since classically several symmetrisers are known to exist