$\mathcal{W}$-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.

46 pages, 2 figures

References in corpus (2)

• Generalized Vertex Algebras
• The Extended Algebra of the Minimal Models