ar X iv : q - a lg / 9 60 90 08 v 1 9 S ep 1 99 6 A three - parameter deformation of the Weyl - Heisenberg algebra : differential calculus and invariance ∗

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 )

h-deformation of (graded) Hopf algebra of functions on supergroup GL(1|1) is introduced via a contration of GL q (1|1). The deformation parameter h is odd (grassmann). Related differential calculus on h-superplane is presented.

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 70 90 01 v 1 1 S ep 1 99 7 Bilinear identity for q - hypergeometric integrals

ar X iv : s ol v - in t / 9 90 60 08 v 1 1 5 Ju n 19 99 PARACONFORMAL STRUCTURES AND INTEGRABLE SYSTEMS

We consider some natural connections which arise between right-flat (p, q) para-conformal structures and integrable systems. We find that such systems may be formulated in Lax form, with a " Lax p-tuple " of linear differential operators, depending a spectral parameter which lives in (q − 1)-dimensional complex projective space. Generally, the differential operators contain partial derivatives ...

ar X iv : q - a lg / 9 60 10 10 v 1 1 1 Ja n 19 96 UAHEP 956 November 1995 TWO - PARAMETER DEFORMATION OF THE POINCARÉ ALGEBRA

We examine a two-parameter (, λ) deformation of the Poincarè algebra which is covariant under the action of SLq(2, C). When λ → 0 it yields the Poincarè algebra, while in the → 0 limit we recover the classical quadratic algebra discussed previously in [1], [2]. The analogues of the Pauli-Lubanski vector w and Casimirs p 2 and w 2 are found and a set of mutually commuting operators is constructed.