Operator algebra

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

Rationality of fixed-point vertex operator algebras

Abstract: We show that if $T$ is a simple regular vertex operator algebra of CFT type with a nonsingular invariant bilinear form and $\sigma$ is a finite automorphism of $T$, then the fixed point vertex operator subalgebra $T^\sigma$ is also regular.

Fock representations from U(1) holonomy algebras

Abstract: We examine the quantization of $U(1)$ holonomy algebras using the Abelian ${C}^{*}$ algebra based techniques which form the mathematical underpinnings of current efforts to construct loop quantum gravity. In particular, we clarify the role of ``smeared loops'' and of Poincar\'e invariance in the construction of Fock representations of these algebras. This enables us to critically reexamine early pioneering efforts to construct Fock space representations of linearized gravity and free Maxwell theory from holonomy algebras through an application of the (then current) techniques of loop quantum gravity.

Nonextendible positive maps

Abstract: Positive maps of ordered vector spaces into the algebra of all bounded operators acting on a Hilbert space are considered. A special class of so called nonextendible maps is introduced and investigated. This class is much smaller than the class of extreme maps.

Vertex operator algebras and associative algebras

Abstract: Let V be a vertex operator algebra. We construct a sequence of associative algebras A_n(V) (n=0,1,2,...) such that A_{n}(V) is a quotient of A_{n+1}(V) and a pair of functors between the category of A_n(V)-modules which are not A_{n-1}(V)-modules and the category of admissible V-modules. These functors exhibit a bijection between the simple modules in each category. We also show that V is rational if and only if all A_n(V) are finite-dimensional semisimple algebras.