SOME REMARKS ON PRODUCING HOPF-ALGEBRAS

We report some observations concerning two well-known approaches to co nstruction of quantum groups. Thus, starting from a bialgebra of inhom ogeneous type and imposing quadratic, cubic or quartic commutation rel ations on a subset of its generators we come, in each case, to a q-def ormed universal enveloping algebra of a certain simple Lie algebra. An interesting correlation between the order of initial commutation rela tions and the Cartan matrix of the resulting algebra is observed. Anot her example demonstrates that the bialgebra structure of sl(q)(2) can be completely determined by requiring the q-oscillator algebra to be i ts covariant comodule, in analogy with Manin's approach to define SL(q )(2) as a symmetry algebra of the bosonic and fermionic quantum planes .