On simplicity of universal minimal W-algebras

TL;DR

This paper investigates the simplicity conditions of universal minimal quantum affine W-algebras and determines the parameters for which the vacuum module over superconformal algebras remains irreducible.

Contribution

It provides new criteria for the simplicity of universal minimal quantum affine W-algebras and identifies specific center values affecting irreducibility.

Findings

Criteria for simplicity of W-algebras established

Center values for irreducibility of vacuum modules identified

Enhanced understanding of superconformal algebra representations

Abstract

Simplicity of universal minimal quantum affine W-algebras is studied. As an application, we find the values of the center, for which the vacuum module over a superconformal algebra is irreducible.