Casimir invariants from quasi-Hopf (super)algebras

We show how to construct, starting from a quasi-Hopf (super)algebra, central elements or Casimir invariants. We show that these central elements are invariant under quasi-Hopf twistings. As a consequence, the elliptic quantum (super)groups, which arise from twisting the normal quantum (super)groups, have the same Casimir invariants as the corresponding quantum (super)groups. (C) 2000 American Institute of Physics. [S0022-2488(99)01312-2]