Related papers: Non-Archimedean Vertex Algebras
A series of nonrepresentable relation algebras is constructed from groups. We use them to prove that there are continuum many subvarieties between the variety of representable relation algebras and the variety of coset relation algebras. We…
Associated varieties of vertex algebras are analogue of the associated varieties of primitive ideals of the universal enveloping algebras of semisimple Lie algebras. They not only capture some of the important properties of vertex algebras…
There is a long-standing problem of algebra to extend the symmetric monoidal structure of abelian groups, given by the tensor product, to a non abelian setting. In this paper we show that such an extension is possible. Morover our non…
We discuss certain ternary algebraic structures appearing more or less naturally in various domains of theoretical and mathematical physics. Far from being exhaustive, this article is intended above all to draw attention to these algebras,…
The representation and the cohomology theory of associative 2-algebras are developed. We study the deformations and abelian extensions of associative 2-algebras in details.
Fermionic zero modes around non-abelian vortices are shown that they constitute two $N=2$, $d=1$ supersymmetric quantum mechanics algebras. These two algebras can be combined under certain circumstances to form a central charge extended…
A general framework for obtaining certain types of contracted and centrally extended algebras is presented. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models.
We introduce and study the notion of a logarithmic vertex algebra, which is a vertex algebra with logarithmic singularities in the operator product expansion of quantum fields; thus providing a rigorous formulation of the algebraic…
We endow categories of non-symmetric operads with natural model structures. We work with no restriction on our operads and only assume the usual hypotheses for model categories with a symmetric monoidal structure. We also study categories…
A version of Auslander theorem is proven for the following classes of noncommutative algebras: (a) noetherian PI local (or connected graded) algebras of finite injective dimension, (b) universal enveloping algebras of finite dimensional Lie…
We propose a classical analogue of the vertex algebra in the context of classical integrable field theories. We use this fundamental notion to describe the auxiliary function of the linear auxiliary problem as a classical vertex operator.…
After an historical introduction on the standard algebraic approach to quantum mechanics of large systems we review the basic mathematical aspects of the algebras of unbounded operators. After that we discuss in some details their relevance…
It is known that there are Lie algebras with non-semigroup gradings, i.e. such that the binary operation on the grading set is not associative. We provide a similar example in the class of associative algebras.
Advances in physics have required the application of more and more sophisticated mathematics. I present arguments supporting the contention that the next advance beyond quantum field theory will require the application of a non-associative…
We give examples of pairs of isotopic algebras with non-isomorphic congruence lattices. This answers the question of whether all isotopic algebras have isomorphic congruence lattices.
Unitary vertex operator algebras are introduced and studied. It is proved that most well-known rational vertex operator algebras are unitary. The classification of unitary vertex operator algebras with central charge c less than or equal to…
We study the representation theory of the infinite type A Hecke algebra over a non-archimedean field in the case where the parameter is a pseudo-uniformizer. Specifically, we consider a family of representations, called almost-symmetric,…
We introduce a new class of possibly infinite dimensional Lie algebras and study their structural properties. Examples of this new class of Lie algebras are finite dimensional simple Lie algebras containing a nonzero split torus, affine and…
This paper illustrates the combinatorial approach to vertex algebra - study of vertex algebras presented by generators and relations. A necessary ingredient of this method is the notion of free vertex algebra. Borcherds \cite{bor} was the…
We describe some aspects of spectral theory that involve algebraic considerations but need no analysis. Some of the important applications of the results are to the algebra of $n\times n$ matrices with entries that are polynomials or more…