ISOMORPHISMS BETWEEN QUANTUM GROUP COVARIANT Q-OSCILLATOR SYSTEMS DEFINED FOR Q AND Q(-1)

It is shown that there exists an isomorphism between q-oscillator systems covariant under SUq(n) and SUq-1(n). By the isomorphism, the defining relations of a SUq-1(n) covariant q-oscillator system are transmuted into those of SUq(n). It is also shown that a similar isomorphism exists for the system of q-oscillators covariant under the quantum supergroup SUq(n/m). Furthermore, the cases of q-deformed Lie (super)algebras constructed from covariant q-oscillator systems are considered. The isomorphisms between q-deformed Lie (super)algebras cannot be obtained by the direct generalization of the isomorphism for covariant q-oscillator systems.