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

ar X iv : q - a lg / 9 60 70 28 v 1 2 7 Ju l 1 99 6 Examples of Categorification

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.

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 60 60 16 v 1 2 3 Ju n 19 96 LIE ALGEBRAS AND THE FOUR COLOR THEOREM DROR

We present a “reasonable” statement about Lie algebras that is equivalent to the Four Color Theorem.

ar X iv : q - a lg / 9 60 70 31 v 1 3 0 Ju l 1 99 6 Level - 0 action of U q ( ŝl n ) on the q - deformed Fock spaces

On the level-1 Fock space modules of the algebra Uq(ŝln) we define a level-0 action U0 of the Uq(ŝln), and an action of an abelian algebra of conserved Hamiltonians commuting with the U0. An irreducible decomposition of the Fock space with respect to the level-0 action is derived by constructing a base of the Fock space in terms of the Non-symmetric Macdonald Polynomials. e-mail: takemura@kurim...