QUANTUM GROUPS SOQ(N), SPQ(N) HAVE Q-DETERMINANTS, TOO

We construct the q-deformed analogue of the completely antisymmetric tensors and the corresponding q-determinants det(q) T for the quantum groups SO(q)(N), SP(q)(n). The construction is based on the existence of the volume form in the algebra of exterior forms on the corresponding quantum spaces. We show that det(q) T is central in Fun(SO(q)(N)) (respectively Fun (Sp(q) (n))) is group-like under the Hopf algebra comultiplication, and that its square is 1.