On invariants of graphs related to quantum sl(2)\mathfrak{sl}(2) at roots of unity

We show how to define invariants of graphs related to quantum $\mathfrak{sl}(2)$ when the graph has more then one connected component and components are colored by blocks of representations with zero quantum dimensions

Lectures on quantization of gauge systems

A gauge system is a classical field theory where among the fields there are connections in a principal G-bundle over the space-time manifold and the classical action is either invariant or transforms appropriately with respect to the action of the gauge group. The lectures are focused on the path integral quantization of such systems. Here two main examples of gauge systems are Yang-Mills and Chern-Simons.Comment: 63 pages, 22 figures. Based on lectures given at the Summer School "New paths towards quantum gravity", Holbaek, Denmark, 200

The Dirac operator and gamma matrices for quantum Minkowski spaces

Gamma matrices for quantum Minkowski spaces are found. The invariance of the corresponding Dirac operator is proven. We introduce momenta for spin 1/2 particles and get (in certain cases) formal solutions of the Dirac equation.Comment: 25 pages, LaTeX fil

Quasitriangularity and enveloping algebras for inhomogeneous quantum groups

Coquasitriangular universal ${\cal R}$ matrices on quantum Lorentz and quantum Poincar\'e groups are classified. The results extend (under certain assumptions) to inhomogeneous quantum groups of [10]. Enveloping algebras on those objects are described.Comment: 18 pages, LaTeX file, minor change

Braiding for the quantum gl_2 at roots of unity

In our preceding papers we started considering the categories of tangles with flat G-connections in their complements, where G is a simple complex algebraic group. The braiding (or the commutativity constraint) in such categories satisfies the holonomy Yang-Baxter equation and it is this property which is essential for our construction of invariants of tangles with flat G-connections in their complements. In this paper, to any pair of irreducible modules over the quantized universal enveloping algebra of gl_2 at a root of unity, we associate a solution of the holonomy Yang-Baxter equation.Comment: 18 pages, 1 figur