Preprint: imsc-94/43

On a nonstandard two-parametric quantum algebra and its connections with U p,q (gl(2)) and U p,q (gl(1|1)) Abstract. A quantum algebra U p,q (ζ, H, X ±) associated with a nonstandard R-matrix with two deformation parameters(p, q) is studied and, in particular, its universal R-matrix is derived using Reshetikhin's method. Explicit construction of the (p, q)-dependent nonstandard R-matrix is obtained through a coloured generalized boson realization of the universal R-matrix of the standard U p,q (gl(2)) corresponding to a nongeneric case. General finite dimensional coloured representation of the universal R-matrix of U p,q (gl(2)) is also derived. This representation, in nongeneric cases, becomes a source for various (p, q)-dependent nonstandard R-matrices. Superization of U p,q (ζ, H, X ±) leads to the super-Hopf algebra U p,q (gl(1|1)). A contraction procedure then yields a (p, q)-deformed super-Heisenberg algebra U p,q (sh(1)) and its universal R-matrix.