Certain Clifford-like algebra and quantum vertex algebras

TL;DR

This paper explores a Clifford-like algebra within quantum vertex algebras, establishing bases, classifying modules, and constructing related quantum vertex algebras, revealing new algebraic structures and module correspondences.

Contribution

It introduces a new algebraic structure and connects modules of Clifford-like algebras with quantum vertex algebra modules, advancing the understanding of their representations.

Findings

Established PBW bases for the Clifford-like algebra

Classified its irreducible modules using Verma modules

Constructed a quantum vertex algebra related to the Clifford-like algebra

Abstract

In this paper, we study in the context of quantum vertex algebras a certain Clifford-like algebra introduced by Jing and Nie. We establish bases of PBW type and classify its $\mathbb N$-graded irreducible modules by using a notion of Verma module. On the other hand, we introduce a new algebra, a twin of the original algebra. Using this new algebra we construct a quantum vertex algebra and we associate $\mathbb N$-graded modules for Jing-Nie's Clifford-like algebra with $\phi$-coordinated modules for the quantum vertex algebra. We also show that the adjoint module for the quantum vertex algebra is irreducible.