ar X iv : q - a lg / 9 50 70 02 v 1 6 J ul 1 99 5 On the non - commutative Riemannian geometry of GL q ( n )

ar X iv : q - a lg / 9 50 70 01 v 1 4 J ul 1 99 5 Link invariants and Combinatorial Quantization of Hamiltonian Chern

We define and study the properties of observables associated to any link in Σ × R (where Σ is a compact surface) using the combinatorial quantization of hamiltonian Chern-Simons theory. These observables are traces of holonomies in a non commutative Yang-Mills theory where the gauge symmetry is ensured by a quantum group. We show that these observables are link invariants taking values in a non...

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 60 50 08 v 1 5 M ay 1 99 6 QUANTUM PRINCIPAL BUNDLES & THEIR CHARACTERISTIC CLASSES

A general theory of characteristic classes of quantum principal bundles is sketched, incorporating basic ideas of classical Weil theory into the conceptual framework of non-commutative differential geometry. A purely cohomological interpretation of the Weil homomorphism is given, together with a geometrical interpretation via quantum invariant polynomials. A natural spectral sequence is describ...

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 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.