arXiv subjects
Publications and source records attributed to Reinhard Häring.
All rational semisimple braided tensor categories are representation categories of weak quasi Hopf algebras. To proof this result we construct for any given category of this kind a weak quasi tensor functor to the category of finite dimensional vector spaces. This allows to reconstruct a weak quasi Hopf algebra with the given category as its representation category.
The representations of the observable algebra of a low dimensional quantum field theory form the objects of a braided tensor category. The search for gauge symmetry in the theory amounts to finding an algebra which has the same representation category. In this paper we try to establish that every quantum field theory satisfying some basic axioms posseses a weak quasi Hopf algebra as gauge symmetry. The first step is to construct a functor from the representation category to the category of finite dimensional vector spaces. Given such a functor we can use a generalized reconstruction theorem to find the symmetry algebra. It is shown how this symmetry algebra is used to build a gauge covariant field algebra and we investigate the question why this generality is necessary.