Related papers: Irregular vertex algebras
Algebras of ultradifferentiable generalized functions are introduced. We give a microlocal analysis within these algebras related to the regularity type and the ultradifferentiable property.
We present a generalization of the notion of an algebra norm relevant to real finite-dimensional unital associative algebras. Among other things, this leads to a novel set of algebra isomorphism invariants, some of which are computationally…
We prove an equivalence between the following notions: (i) unitary M\"obius vertex algebras, and (ii) Wightman conformal field theories on the circle (with finite-dimensional conformal weight spaces) satisfying an additional condition that…
The notion of singular reduction operators, i.e., of singular operators of nonclassical (conditional) symmetry, of partial differential equations in two independent variables is introduced. All possible reductions of these equations to…
We develop here a concept of deformed algebras through three examples and an application. Deformed algebras are obtained from a fixed algebra by deformation along a family of indexes, through formal series. We show how the example of…
We give the operadic formulation of (weak, strong) topological vertex algebras, which are variants of topological vertex operator algebras studied recently by Lian and Zuckerman. As an application, we obtain a conceptual and geometric…
Vertex operators for the deformed Virasoro algebra are defined, their bosonic representation is constructed and difference equation for the simplest vertex operators is described.
We survey the operator algebras arising as commutants modulo normed ideals of finite sets of hermitian operators and connections to perturbations of operators and noncommutative geometry.
We expand on some invariants used for classifying nonselfadjoint operator algebras. Specifically to nonselfadjoint operator algebras which have a conditional expectation onto a commutative diagonal we construct an edge-colored directed…
We present alternative postulates for Euclidean geometry whose merit is that they lead to a new class of invariants and associated geometries for real finite-dimensional unital associative algebras.
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.
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
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 paper we develop a formalism for working with twisted realizations of vertex and conformal algebras. As an example, we study realizations of conformal algebras by twisted formal power series. The main application of our technique is…
A higher dimensional analogue of the notion of vertex algebra is formulated in terms of formal variable language with Borcherds' notion of $G$-vertex algebra as a motivation. Some examples are given and certain analogous duality properties…
: Algebraic properties of orbifold models on arbitrary Riemann surfaces are investigated. The action of mapping class group transformations and of standard geometric operations is given explicitly. An infinite dimensional extension of the…
Huang's geometric interpretation of vertex operator algebras is extended to a supergeometric interpretation of vertex operator superalgebras. In particular, the geometry of spheres with punctures and local analytic coordinates in terms of…
By considering generalized logarithm and exponential functions used in nonextensive statistics, the four usual algebraic operators : addition, subtraction, product and division, are generalized. The properties of the generalized operators…
We propose a conjectural correspondence between the spectra of the Bethe algebra for the quantum toroidal $\mathfrak{gl}_2$ algebra on relaxed Verma modules, and $q$-hypergeometric opers with apparent singularities. We introduce alongside…
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…