ar X iv : q - a lg / 9 51 10 09 v 2 1 7 D ec 1 99 5 h - deformation of GL ( 1 | 1 )

ar X iv : q - a lg / 9 70 50 27 v 1 2 8 M ay 1 99 7 Jordanian U h , s gl ( 2 ) and its coloured realization

A two-parametric non-standard (Jordanian) deformation of the Lie algebra gl(2) is constructed, and then, exploited to obtain a new, triangular R-matrix solution of the coloured Yang-Baxter equation. The corresponding coloured quantum group is presented explicitly.

ar X iv : q - a lg / 9 51 10 18 v 1 2 3 N ov 1 99 5 Unitary operator bases and q - deformed algebras

Starting from the Schwinger unitary operator bases formalism constructed out of a finite dimensional state space, the well-known q-deformed commu-tation relation is shown to emerge in a natural way, when the deformation parameter is a root of unity.

ar X iv : q - a lg / 9 70 60 09 v 1 1 1 Ju n 19 97 q - Deformation of the Krichever - Novikov Algebra

Using q-operator product expansions between U (1) current fields and also the corresponding energy-momentum tensors, we furnish the q-analoques of the generalized Heisenberg algebra and the Krichever-Novikov algebra.

ar X iv : q - a lg / 9 61 20 14 v 1 1 1 D ec 1 99 6 Integral soluitons of q - difference equations

Two integral solutions of q-difference equations of the hypergeometric type with |q| = 1 are constructed by using the double sine function. One is an integral of the Barnes type and the other is of the Euler type.

ar X iv : m at h / 99 07 08 5 v 2 [ m at h . G R ] 1 7 D ec 1 99 9 LOOPS AND SEMIDIRECT PRODUCTS