Simplicity of vacuum modules and associated varieties

Abstract

In this note, we prove that the universal affine vertex algebra associated with a simple Lie algebra $\mathfrak{g}$ is simple if and only if the associated variety of its unique simple quotient is equal to ${\mathfrak{g}}^{\ast }$. We also derive an analogous result for the quantized Drinfeld-Sokolov reduction applied to the universal affine vertex algebra.

arXiv comment21 pages in English

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Cited by in corpus (2)

• Galilean $W_3$ algebra
• Associated varieties of simple affine VOAs $L_k(s{l}_3)$ and $W$-algebras $W_k(s{l}_3,f)$