Authors: Dražen Adamović, Victor G. Kac, Pierluigi Möseneder Frajria, Paolo Papi, Ozren Perše

Journal of Algebra,

Volume 500,

2018,

Pages 117-152,

ISSN 0021-8693,

https://doi.org/10.1016/j.jalgebra.2016.12.005

(http://www.sciencedirect.com/science/article/pii/S0021869316304604)

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