Related papers: Genus of vertex algebras and mass formula
The notion of the genus of a quadratic form is generalized to vertex operator algebras. We define it as the modular braided tensor category associated to a suitable vertex operator algebra together with the central charge. Statements…
We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.
In this paper we try to define the higher dimensional analogues of vertex algebras. In other words we define algebras which we hope have the same relation to higher dimensional quantum field theories that vertex algebras have to one…
The purpose of this paper is to make the theory of vertex algebras trivial. We do this by setting up some categorical machinery so that vertex algebras are just ``singular commutative rings'' in a certain category. This makes it easy to…
This book offers an introduction to vertex algebra based on a new approach. The new approach says that a vertex algebra is an associative algebra such that the underlying Lie algebra is a vertex Lie algebra. In particular, vertex algebras…
This paper illustrates the combinatorial approach to vertex algebra - study of vertex algebras presented by generators and relations. A necessary ingredient of this method is the notion of free vertex algebra. Borcherds \cite{bor} was the…
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…
In this article, we completely determine the isomorphism classes of lattice vertex operator algebras and the vertex operator subalgebras fixed by a lift of the -1-isometry of the lattice. We also provide similar results for certain even…
In this paper we build an abstract description of vertex algebras from their basic axioms. Starting with Borcherds' notion of a vertex group, we naturally construct a family of multilinear singular maps parameterised by trees. These…
We associate to any holomorphic vertex algebra a collection of Teichm\"{u}ller modular forms, one in each genus. In genus one we obtain the character of the vertex algebra, and we thus reprove Zhu's modularity result. In higher genus, we…
In this note we give an account of recent progress on the construction of holomorphic vertex algebras as cyclic orbifolds as well as related topics in lattices and modular categories. We present a novel computation of the Schur indicator of…
We associate elliptic affine Lie algebras with what are called vertex $\C((z))$-algebras and their modules in a certain category. In the course, we construct two families of Lie algebras closely related to elliptic affine Lie algebras.
In this paper we study the representation theory for certain ``half lattice vertex algebras.'' In particular we construct a large class of irreducible modules for these vertex algebras. We also discuss how the representation theory of these…
In this paper we introduce a notion of vertex Lie algebra U, in a way a "half" of vertex algebra structure sufficient to construct the corresponding local Lie algebra L(U) and a vertex algebra V(U). We show that we may consider U as a…
We develop a theory of toroidal vertex algebras and their modules, and we give a conceptual construction of toroidal vertex algebras and their modules. As an application, we associate toroidal vertex algebras and their modules to toroidal…
The notion of {\it free} generalized vertex algebras is introduced. It is equivalent to the notion of {\it generalized principal subspaces} associated with lattices which are not necessarily integral. Combinatorial bases and the characters…
The notion of vertex operator coalgebra is presented and motivated via the geometry of conformal field theory. Specifically, we describe the category of geometric vertex operator coalgebras, whose objects have comultiplicative structures…
The notions of vertex Lie algebra and vertex Poisson algebra are presented and connections among vertex Lie algebras, vertex Poisson algebras and vertex algebras are discussed.
We give an interpretation of the cohomology of an arithmetically defined group as a set of equivalence classes of lattices. We use this interpretation to give a simpler proof of the connection established by J. Rohlfs between genus and…
On the vertex operator algebra associated with rank one lattice we derive a general formula for products of vertex operators in terms of generalized homogeneous symmetric functions. As an application we realize Jack symmetric functions of…