Related papers: Some developments in vertex operator algebra theor…
In this paper, we study the algebra of twisted vertex operators over an even integral ${\mathbf Z}_2$-lattice, and give a kind of systematic construction of fundamental representations for affine Lie algebras of type $A$, $D$, $E$ with…
The connection between Riemann surfaces with boundaries and the theory of vertex operator algebras is discussed in the framework of conformal field theories defined by Kontsevich and Segal and in the framework of their generalizations in…
For certain vertex operator algebras (e.g., lattice type) and given finite group of automorphisms, we prove existence of a positive definite integral form invariant under the group. Applications include an integral form in the Moonshine VOA…
We classify vertex operator algebras (VOAs) of OZ-type generated by Ising vectors of $\sigma$-type. As a consequence of the classification, we also prove that such VOAs are simple, rational, $C_2$-cofinite and unitary, that is, they have…
We discuss several open problems on spectrally bounded operators, some new, some old, adding in a few new insights.
The extensions of the affine vertex operator algebras $L_{sl_2}(k,0)$ and the preunitary vertex operator algebras with central charges $c<1$ are classified. In particular, the unitary vertex operator algebras with central charges $c<1$ are…
The present text surveys some relevant situations and results where basic Module Theory interacts with computational aspects of operator algebras. We tried to keep a balance between constructive and algebraic aspects.
We establish the various properties as well as diverse relations of the ascent and descent spectra for bounded linear operators. We specially focus on the theory of subspectrum. Furthermore, we construct a new concept of convergence for…
The purpose of this paper is to introduce the cohomology of various algebras over an operad of moduli spaces including the cohomology of conformal field theories (CFT's) and vertex operator algebras (VOA's). This cohomology theory produces…
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 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 algebraic deformation theory of algebras over the Landweber-Novikov algebra is obtained.
We provide a brief survey of a certain algebra of operators on symmetric polynomials, and collect a number of previously known results in the field.
This article gives a brief introduction to some recent work on deformation and homotopy theories of Rota-Baxter operators and more generally $\mathcal{O}$-operators on Lie algebras, by means of the differential graded Lie algebra approach.…
After giving some definitions for vertex operator SUPERalgebras and their modules, we construct an associative algebra corresponding to any vertex operator superalgebra, such that the representations of the vertex operator algebra are in…
We introduce operational semantics into games. And based on the operational semantics, we establish a full algebra of games, including basic algebra of games, algebra of concurrent games, recursion and abstraction. The algebra can be used…
The well known operator ordering ambiguity could motivate the existence of generations. This possibility is explored by exploiting the relationship between ordering and discretization rules. Context is drawn from lattice theory and non…
We study connections between closure operators on an algebra $(A,\Om)$ and congruences on the extended power algebra defined on the same algebra. We use these connections to give an alternative description of the lattice of all subvarieties…
In this text, we wish to provide the reader with a short guide to recent works on the theory of dilatations in Commutative Algebra and Algebraic Geometry. These works fall naturally into two categories: one emphasises foundational and…
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…