Authors: Dražen Adamović, Victor G. Kac, Pierluigi Möseneder Frajria, Paolo Papi, Ozren Perše
Journal of Algebra,
Abstract: We find all values of , for which the embedding of the maximal affine vertex algebra in a simple minimal W-algebra is conformal, where ,is a basic simple Lie superalgebra and its minimal root. In particular, it turns out that if does not collapse to its affine part, then the possible values of these k are either or , where is the dual Coxeter number of for the normalization . As an application of our results, we present a realization of simple affine vertex algebra inside the tensor product of the vertex algebra (also called the Bershadsky–Knizhnik algebra) with a lattice vertex algebra.
Keywords: Vertex algebra; Virasoro (=conformal) vector; Conformal embedding; Conformal level; Collapsing level