Operator algebra

About: Operator algebra is a research topic. Over the lifetime, 5783 publications have been published within this topic receiving 165303 citations.

Skeins and handlebodies

Abstract: The Temperley-Lieb algebra is used to find a base for the vector space that is associated to a closed surface by the Topological Quantum Field Theory corresponding to the original Jones polynomial invariant

A Finite Dimensional Introduction to Operator Algebra

Abstract: This article surveys some recent advances in operator algebra that were inspired by considerations from ring theory, particularly the representation theory of finite dimensional algebras.

Diffeomorphism groups and current algebras: configuration space analysis in quantum theory

Abstract: The constuction of models of non-relativistic quantum fields via current algebra representations is presented using a natural differential geometry of the configuration space Γ of particles, the corresponding classical Dirichlet operator associated with a Poisson measure on Γ, being the free Hamiltonian. The case with interactions is also discussed together with its relation to the problem of unitary representations of the diffeomorphism group on ℝd.

On the causal structure of Minkowski spacetime

Abstract: The causal structure of Minkowski spacetime M is discussed, in terms of the notions of causal complementation and causal completion. These geometric notions are relevant for quantum field theory and the theory of the Klein-Gordon equation. Particular attention is given to closed, convex, causally complete subsets of M, and the properties of such sets are discussed. The study of such sets is motivated by potential applications to the theory of local nets of von Neumann algebras. The notion of the envelope of uniqueness of a subset of M, familiar from the theory of the wave equation, is discussed, and some results about the relation of this envelope to the causal completion of the set are presented.

Algebras generated by idempotents and the symbol calculus for singular integral operators

Abstract: It is proved that in Banach algebras generated by two idempotents and, perhaps, by a certain flip operator the standard identity F4 is fulfilled. The maximal ideal space of such algebras is determined and the corresponding symbol is given. By means of local techniques these results are applied to obtain a symbol calculus for singular integral operators with Carleman shift (changing the orientation) in weighted Banach spaces.