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$\mathcal{W}$-algebras with non-admissible levels and the Deligne exceptional series (1505.06985v1)
Published 26 May 2015 in math.QA, math-ph, math.MP, and math.RT
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.
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