Related papers: Local and Semilocal Vertex Operator Algebras

Given a collection of modules of a vertex algebra parametrized by an abelian group, together with one dimensional spaces of composable intertwining operators, we assign a canonical element of the cohomology of an Eilenberg-Mac Lane space.…

While there is a well developed theory of locally solid topologies, many important convergences in vector lattice theory are not topological. Yet they share many properties with locally solid topologies. Building upon the theory of…

Two extension problems are solved. First, the class of locally matricial algebras over an arbitrary field is closed under extensions. Second, the class of locally finite dimensional semisimple algebras over a fixed field is closed under…

It is shown that a simple vertex operator algebra V is rational if and only if its Zhu algebra A(V) is semisimple and each irreducible admissible V-module is ordinary. A contravariant form on a Verma type admissible V-module is constructed…

We prove a generalized rationality property and a new identity that we call the ``Jacobi identity'' for intertwining operator algebras. Most of the main properties of genus-zero conformal field theories, including the main properties of…

An associative ring with 1 is said to be semilocal provided it is semisimple artinian modulo its Jacobson radical, that is, modulo its Jacobson radical it is isomorphic to a finite product of matrices over division rings. Modules with a…

The rational and C_2-cofinite simple vertex operator algebras whose effective central charges and the central charges c are equal and less than 1 are classified. Such a vertex operator algebra is zero if c<0 and C if c=0. If c>0, it is an…

Using representation theory techniques we prove that various spaces of derivations or one-sided multipliers over certain operator algebras are reflexive. A sample result: any bounded local derivation (local left multiplier) on an…

We consider semigroups of operators on a W$^*$-algebra and prove, under appropriate assumptions, the existence of a Jacobs-DeLeeuw-Glicksberg type decomposition. This decomposition splits the algebra into a "stable" and "reversible" part…

A notion of local algebras is introduced in the theory of causal fermion systems. Their properties are studied in the example of the regularized Dirac sea vacuum in Minkowski space. The commutation relations are worked out, and the…

This paper studies the twisted representations of vertex operator algebras. Let V be a vertex operator algebra and g an automorphism of V of finite order T. For any m,n in (1/T)Z_+, an A_{g,n}(V)-A_{g,m}(V)-bimodule A_{g,n,m}(V) is…

We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar…

We prove a conjecture stated in a previous paper by the author about the existence of canonical filtrations for a family of vertex operator algebras in rational levels.

Using general principles of the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie algebra of differential operators on the circle, for an…

Given a weight-one element $u$ of a vertex operator algebra $V$, we construct an automorphism of the category of generalized $g$-twisted modules for automorphisms $g$ of $V$ fixing $u$. We apply this construction to the case that $V$ is an…

We study vertex algebras and their modules associated with possibly degenerate even lattices, using an approach somewhat different from others. Several known results are recovered and a number of new results are obtained. We also study…

We consider functors from the category of locally convex algebras to abelian groups and prove invariance under smooth homotopies for weakly J-stable algebras, where J is a harmonic operator ideal. This applies in particular to negative…

We give a short introduction to generalized vertex algebras, using the notion of polylocal fields. We construct a generalized vertex algebra associated to a vector space h with a symmetric bilinear form. It contains as subalgebras all…

Using recursion formulas for vertex operator algebra higher genus characters with formal parameters identified with local coordinates around marked points on a Riemann surface of arbitrary genus, we introduce the notion of a vertex operator…

The purpose of this work is to illustrate in a family of interesting examples how to study the representation theory of vertex operator superalgebras by combining the theory of vertex algebra extensions and modular forms. Let…