Related papers: Irregular vertex algebras
We construct bundles of modules of vertex operator algebras, and prove the rigidity and vanishing theorem for the Dirac operator on loop space twisted by such bundles. This result generalizes many previous results.
We assume that every element of a matrix has a small, individual error, and model it by an external number, which is the sum of a nonstandard real number and a neutrix, the latter being a convex (external) set having the group property. The…
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…
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…
We develop the notion of deformations using a valuation ring as ring of coefficients. This permits to consider in particular the classical Gerstenhaber deformations of associative or Lie algebras as infinitesimal deformations and to solve…
We construct supersymmetric irregular vertex operators of arbitrary rank, appearing in the colliding limit of primary fields. We find that the structure of the supersymmetric irregular vertices differs significantly from the bosonic case:…
Starting from a biased definition of a properad, we describe explicitly algebras over the cobar construction of a properad. Equivalent description in terms of solutions of generalized master equations, which can be interpreted as…
We study twisted modules for (weak) quantum vertex algebras and we give a conceptual construction of (weak) quantum vertex algebras and their twisted modules. As an application we construct and classify irreducible twisted modules for a…
We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…
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…
Vertex $F$-algebras are a deformation of the concept of an ordinary vertex algebra in which the additive formal group law is replaced by an arbitrary formal group law $F$. The main theorem of this paper constructs a Lie algebra from a…
In this paper, we give a purely cohomological interpretation of the extension problem for associative algebras; that is the problem of extending an associative algebra by another associative algebra. We then give a similar interpretation of…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…
There are many analogies between codes, lattices, and vertex operator algebras. For example, extremal objects are good examples of combinatorial, spherical, and conformal designs. In this study, we investigated these objects from the aspect…
Inverse spectral problems are studied for the second order integro-differential operators on a finite interval. Properties of spectral characteristic are established, and the uniqueness theorem is proved for this class of inverse problems.
A series of vertex operator algebras are constructed by GKO-construction, which is a generalization of 3A-algebra and 6A-algebra. It is proved their vertex operator algebra structures are unique under nonzero assumptions on some elements of…
We introduce the notion of a genus and its mass for vertex algebras. For lattice vertex algebras, their genera are the same as those of lattices, which plays an important role in the classification of lattices. We derive a formula relating…
An extension of the General Coordinate Transformations algebra is constructed by means geometrical consistency conditions. An class of infinite invariants is derived. In particular we construct the consistent extension of the gravitational…
We introduce a notion of planar algebra, the simplest example of which is a vector space of tensors, closed under planar contractions. A planar algebra with suitable positivity properties produces a finite index subfactor of a II_1 factor,…