  We study the various term operations on the set of skew primitive elements of
Hopf algebras, generated by skew primitive semi-invariants of an Abelian group
of grouplike elements. All 1-linear binary operations are described and
trilinear and quadrilinear operations are given a detailed treatment. Necessary
and sufficient conditions for the existence of multilinear operations are
specified in terms of the property of particular noncommutative polynomials
being linearly dependent and of one arithmetic condition. We dub the conjecture
that this condition implies, in fact, the linear dependence of the polynomials
in question and so is itself sufficient (a proof of this conjecture see in "An
existence condition for multilinear quantum operations," Journal of Algebra,
217, 1999, 188-228).
