Related papers: Some developments in vertex operator algebra theor…
We summarize interactions between vertex operator algebras and number theory through the lens of Zhu theory. The paper begins by recalling basic facts on vertex operator algebras (VOAs) and modular forms, and then explains Zhu's theorem on…
Vertex operator superalgebras are studied and various results on rational Vertex operator superalgebras are obtained. In particular, the vertex operator super subalgebras generated by the weight 1/2 and weight 1 subspaces are determined. It…
We change the definition of the vertex representations. As a result the vertex representations has one parameter.
Algebraic properties of $n$-place opening operations on a fixed set are described. Conditions under which a Menger algebra of rank $n$ can be represented by $n$-place opening operations are found.
We give a survey of how the relatively young theory of operator spaces has led to a deeper understanding of the Fourier algebra of a locally compact group (and of related algebras).
For a vertex operator algebra V, a V-module M and a nonnegative integer n, an A_n(V)-bimodule A_n(M) is constructed and studied. The connection between A_n(M) and intertwining operators are discussed. In the case that V is rational, A_n(M)…
The survey contains a brief description of the ideas, constructions, results, and prospects of the theory of hypergroups and generalized translation operators. Representations of hypergroups are considered, being treated as continuous…
The operator algebra is introduced based on the framework of logarithmic representation of infinitesimal generators. In conclusion a set of generally-unbounded infinitesimal generators is characterized as a module over the Banach algebra.
A characterization of vertex operator algebra $V_L^+$ for any rank one positive definite even lattice $L$ is given in terms of dimensions of homogeneous subspaces of small weights. This result reduces the classification of rational vertex…
We define an extension of operator-valued positive definite functions from the real or complex setting to topological algebras, and describe their associated reproducing kernel spaces. The case of entire functions is of special interest,…
This survey provides an elementary introduction to operads and to their applications in homotopical algebra. The aim is to explain how the notion of an operad was prompted by the necessity to have an algebraic object which encodes higher…
Using techniques from the theory of mock modular forms and harmonic Maass forms, especially Weierstrass mock modular forms, we establish several dimension formulas for certain strongly rational, holomorphic vertex operator algebras,…
This is a set of lecture notes on the operator algebraic approach to 2-dimensional conformal field theory. Representation theoretic aspects and connections to vertex operator algebras are emphasized. No knowledge on operator algebras or…
In this paper we explore a new method of analysis of associative algebras.
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.
We develop elements of a general dilation theory for operator-valued measures and bounded linear maps between operator algebras that are not necessarily completely-bounded. We prove our main results by extending and generalizing some known…
We describe a new link between the theory of topological modular forms and representations of vertex operator algebras obtained by certain lattices. The construction is motivated by the arithmetic Whitehead tower of the orthogonal groups.…
We review definitions and basic properties of operads, PROPs and algebras over these structures.
Using general principles in 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…
The vertex operator algebras and modules associated to the highest weight modules for the Virasoro algebra over an arbitrary field F whose characteristic is not equal to 2 are studied. The irreducible modules of vertex operator algebra…