$\mathcal{W}$-algebras with non-admissible levels and the Deligne exceptional series
arXiv:1505.06985
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