Related papers: Non-Archimedean Vertex Algebras

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…

A field algebra is a ``non-commutative'' generalization of a vertex algebra. In this paper we develop foundations of the theory of field algebras.

We survey commutative and non-commutative analogs of uniform algebras in the Archimedean settings and also offer some non-Archimedean examples. Constraints on the development of non-complex uniform algebras are also discussed.

Differentiations of operator algebras over non-archimedean spherically complete fields are investigated. Theorems about a differentiation being internal are demonstrated.

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…

Cohomologies of nonassociative metagroup algebras are investigated. Extensions of metagroup algebras are studied. Examples are given.

An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.

This is a brief review article of various applications of non-Archimedean geometry, p-adic numbers and adeles in modern mathematical physics.

We complete a classification of the two-vertex geometrically irreducible algebras. We also classify the algebras in new classes of hom- and ext-irreducible algebras.

Vertex algebras can be defined over any differential commutative ring. We develop the general descent theory for vertex algebras over such bases. We apply this to the classification of twisted forms of affine and Heisenberg vertex algebras,…

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.

We give a survey on the developments in a certain theory of quantum vertex algebras, including a conceptual construction of quantum vertex algebras and their modules and a connection of double Yangians and Zamolodchikov-Faddeev algebras…

This note surveys basic topological properties of nonarchimedean analytic spaces, in the sense of Berkovich, including the recent tameness results of Hrushovski and Loeser. We also discuss interactions between the topology of nonarchimedean…

We introduce the notion of irregular vertex (operator) algebras. The irregular versions of fundamental properties, such as Goddard uniqueness theorem, associativity and operator product expansions are formulated and proved. We also give…

The mirror extensions for vertex operator algebras are studied. Two explicit examples which are not simple current extensions of some affine vertex operator algebras of type $A$ are given.

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.

Within the concept of a non-Archimedean operator algebra with the Baer reduction (A. N. Kochubei, On some classes of non-Archimedean operator algebras, Contemporary Math. 596 (2013), 133--148), we consider algebras of operators on Banach…

In this exposition, I discuss several developments in the theory of vertex operator algebras, and I include motivation for the definition.

Axial algebras are a recently introduced class of non-associative algebra motivated by applications to groups and vertex-operator algebras. We develop the structure theory of axial algebras focussing on two major topics: (1) radical and…

The article is devoted to the investigation of properties of quasi-invariant measures with values in non-Archimedean fields such as: convolutions of measures and functions; continuity of functions of measures; non-associative noncommutative…