Related papers: What is a vertex algebra?

For a given variety Var of algebras we define the variety Var of dialgebras. This construction turns to be closely related with varieties of pseudo-algebras: every Var-dialgebra can be embedded into an appropriate pseudo-algebra of the…

This is a survey on stated skein algebras and their representations.

Let $G$ be a finite, simple, and undirected graph of order $n$ and average degree $d$. Up to terms of smaller order, we characterize the minimal intervals $I$ containing $d$ that are guaranteed to contain some vertex degree. In particular,…

We view difference algebra as the study of algebraic objects in the topos of difference sets. The methods of topos theory and categorical logic enable us to develop difference homological algebra, identify a solid foundation for difference…

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…

This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry, noncommutative geometry, and theoretical physics are…

The aim of this short survey is to trace back the ingredients going into the derived equivalence classification of Brauer graph algebras and into the proof of the fact that these algebras are closed under derived equivalence.

A description of group automorphisms of all two-dimensional algebras, considered up to isomorphism, over any basic field is provided.

The goal of this article is to describe several presentations of the infinity category of algebras over some monad on the infinity category of chain complexes.

We study the properties of shifted vertex operator algebras, which are vertex algebras derived from a given theory by shifting the conformal vector. In this way, we are able to exhibit large numbers of vertex operator algebras which are…

A notion of intermediate vertex subalgebras of lattice vertex operator algebras is introduced, as a generalization of the notion of principal subspaces. Bases and the graded dimensions of such subalgebras are given.As an application, it is…

This is an extended abstract of my talk at the Oberwolfach-Workshop "Representation Theory of Finite-Dimensional Algebras" (February 6 - 12, 2005). It gives self-contained and simplified definitions of quantum cluster algebras introduced…

We define vertex cover algebras for weighted simplicial multicomplexes and prove basics properties of them. Also, we describe these algebras for multicomplexes which have only one maximal facet and we prove that they are finitely generated.

We give a brief survey of recent work on integral forms in vertex operator algebras (VOAs).

We develop a random model for relation algebras. We prove some preliminary results and pose questions that lay out a new direction of research.

The radical of a vertex operator algebra associated to a module is defined and computed.

We introduce notions of open-string vertex algebra, conformal open-string vertex algebra and variants of these notions. These are ``open-string-theoretic,'' ``noncommutative'' generalizations of the notions of vertex algebra and of…

We introduce the notion of almost finite dimensionality of algebras and study its connection with the classical finiteness conditions.

The usual vertex algebras have as underlying symmetry the Hopf algebra $H_D=\mathbb C[D]$ of infinitesimal translations. We show that it is possible to replace $H_D$ by another symmetry algebra $H_T=\mathbb C[T,T\inv]$, the group algebra of…

In the present paper we obtain the list of algebras, up to isomorphism, such that closure of any complex finite-dimensional algebra contains one of the algebra of the given list.