Related papers: Constructing quantum vertex algebras

In this paper, we associate the quantum toroidal algebra $\mathcal{E}_N$ of type $\mathfrak{gl}_N$ with quantum vertex algebra through equivariant $\phi$-coordinated quasi modules. More precisely, for every $\ell\in \mathbb{C}$, by…

$q$-vertex operators for quantum affine algebras have played important role in the theory of solvable lattice models and the quantum Knizhnik-Zamolodchikov equation. Explicit constructions of these vertex operators for most level one…

In this paper, we study a notion of what we call vertex Leibniz algebra. This notion naturally extends that of vertex algebra without vacuum, which was previously introduced by Huang and Lepowsky. We show that every vertex algebra without…

In this paper, we give a construction of a (C*-algebraic) quantum Heisenberg group. This is done by viewing it as the dual quantum group of the specific non-compact quantum group (A,\Delta) constructed earlier by the author. Our definition…

This is a paper in a series to study vertex algebra-like structures arising from various algebras including quantum affine algebras and Yangians. In this paper, we develop a theory of what we call (weak) quantum vertex $\F((t))$-algebras…

A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large…

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 construct families of commutative (super) algebra objects in the category of weight modules for the unrolled restricted quantum group $\overline{U}_q^H(\mfg)$ of a simple Lie algebra $\mfg$ at roots of unity, and study their categories…

This paper is the first in a series of papers developing a functional-analytic theory of vertex (operator) algebras and their representations. For an arbitrary Z-graded finitely-generated vertex algebra (V, Y, 1) satisfying the standard…

By using the ideas of Feigin and Stoyanovsky and Calinescu, Lepowsky and Milas we introduce and study the principal subspaces associated with the Etingof-Kazhdan quantum affine vertex algebra of integer level $k\geqslant 1$ and type…

Quantum N-toroidal algebras are generalizations of quantum affine algebras and quantum toroidal algebras. In this paper we construct a level-one vertex representation of the quantum N-toroidal algebra for type C. In particular, we also…

It is proved that for a vector space W, any set of parafermion-like vertex operators on W in a certain canonical way generates a generalized vertex algebra in the sense of [DL2] with W as a natural module. This result generalizes a result…

We prove a number of results having to do with equipping type-I $\mathrm{C}^*$-algebras with compact quantum group structures, the two main ones being that such a compact quantum group is necessarily co-amenable, and that if the…

In this paper the q-deformed $W$ algebra $\WW_q$ is constructed, whose nontrivial quantum group structure is presented.

This paper is about establishing a natural connection of quantum affine algebras with quantum vertex algebras. Among the main results, we establish $\hbar$-adic versions of the smash product construction of quantum vertex algebras and their…

Inspired by the Borcherds' work on ``$G$-vertex algebras,'' we formulate and study an axiomatic counterpart of Borcherds' notion of $G$-vertex algebra for the simplest nontrivial elementary vertex group, which we denote by $G_{1}$.…

We study the family of vertex algebras associated with vertex algebroids, constructed by Gorbounov, Malikov, and Schechtman. As the main result, we classify all the (graded) simple modules for such vertex algebras and we show that the…

The mathematical formalism for linear quantum field theory on curved spacetime depends in an essential way on the assumption of global hyperbolicity. Physically, what lie at the foundation of any formalism for quantization in curved…

Certain deformable families of vertex algebras acquire at a limit of the deformation parameter a large center, similar to affine Lie algebras at critical level. Then the vertex algebra and its representation category become a bundle over…

We study quantum current algebra $\textrm{A}(\overline{R})$ associated with the rational $R$-matrix of $\mathfrak{gl}_N$ and we give explicit formulae for the elements of its center at the critical level. Due to Etingof--Kazhdan's…