$\mathcal{W}$-algebras with non-admissible levels and the Deligne exceptional series

Abstract

Structure of certain simple $\mathcal{W}$-algebras assocated with the Deligne exceptional Lie algebras and non-admissible levels are described as the {\it simple current extensions} of certain vertex operator algebras. As an application, the $C_2$-cofiniteness and ${\mathbb{Z}}_2$-rationality of the algebras are proved.

arXiv comment46 pages, 2 figures

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Cited by in corpus (6)

• Conformal embeddings of affine vertex algebras in minimal $W$-algebras I: structural results
• Universal two-parameter even spin ${\mathcal{W}}_{\infty }$-algebra
• Introduction to W-algebras and their representation theory
• On rationality for $C_2$-cofinite vertex operator algebras
• Vertex Algebras and Commutative Algebras
• Modular linear differential equations of fourth order and minimal $\mathcal{W}$-algebras