NONSTANDARD QUANTUM GROUPS AND SUPERIZATION

We obtain the universal R-matrix of the nonstandard quantum group asso ciated to the Alexander-Conway knot polynomial. We show further that t his nonstandard quantum group is related to the super-quantum group U- q gl(1/1) by a general process of superization, which we describe. We also study a twisted variant of this nonstandard quantum group and obt ain, as a result, a twisted version of U-q gl(1/1) as a q supersymmetr y of the exterior differential calculus of any quantum plane of Hecke type, acting by mixing the bosonic x(i) coordinates and the forms dx(i ). (C) 1995 American Institute of Physics.