In this paper, we study the higher Yang-Mills theory in framework of gauge theory. It was shown that 2-form electromagnetism can be generalized to with group U(1) replaced by a crossed module Lie groups. To extend even structure, develop 3-form 2-crossed First, give an explicit construction non-degenerate symmetric G-invariant forms on algebras. Then, derive 3-Bianchi-Identities for 3-curvature...

In this text we use the quantum double construction to show that a suitable category of finite dimensional left U -modules is braided, where U is the quantized universal enveloping algebra of sl2(k). We produce the expression of the corresponding braiding as the action of a formal universal R-matrix for U . We indicate the generalization to sln(k) and the relation to Hecke algebras and Temperle...

Abstract. In this paper we study the tensor category structure of the module category of the restricted quantum enveloping algebra associated to sl2. Indecomposable decomposition of all tensor products of modules over this algebra is completely determined in explicit formulas. As a by-product, we show that the module category of the restricted quantum enveloping algebra associated to sl2 is not...

We give a general integration prescription for finite dimensional braided Hopf algebras, deriving the N-dimensional quantum superplane integral as an example. The transformation properties of the integral on the quantum plane are found. We also discuss integration on quantum group modules that lack a Hopf structure. ENSLAPP-A-562/95 December 1995 URA 14-36 du CNRS, associée à l’Ecole Normale Su...

Results on the niteness of induced crossed modules are proved both algebraically and topologically Using the Van Kampen type theorem for the fundamen tal crossed module applications are given to the types of mapping cones of classifying spaces of groups Calculations of the cohomology classes of some nite crossed modules are given using crossed complex methods Introduction Crossed modules were i...

In this thesis, we use string diagrams to study the theory of Hopf algebras in the context of Categorical Quantum Mechanics. First, we treat the theory of representations of a Hopf algebra diagrammatically. The category of representations of a quasitriangular Hopf algebra Rep(H) is a braided tensor category and can be understood as a process theory of particles in Topological Quantum theory. We...

Following Ellis, [9], we investigate the notion of totally free crossed square and related squared complexes. It is shown how to interpret the information in a free simplicial group given with a choice of CW-basis, interms of the data for a totally free crossed square. Results of Ellis then apply to give a description in terms of tensor products of crossed modules. The paper ends with a purely ...

In this paper we give a construction of free 2-crossed modules. By the use of a `step-by-step' method based on the work of Andr e, we will give a description of crossed algebraic models for the steps in the construction of a free simplicial resolution of an algebra. This involves the introduction of the notion of a free 2-crossed module of algebras.

We obtain some explicit calculations of crossedQ-modules induced from a crossed module over a normal subgroup P of Q. By virtue of theorems of Brown and Higgins, this enables the computation of the homotopy 2-types and second homotopy modules of certain homotopy pushouts of maps of classifying spaces of discrete groups. Introduction A crossed module M = (μ : M → P ) has a classifying space BM (...