{"paper":{"title":"Conformal embeddings of affine vertex algebras in minimal $W$-algebras I: structural results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Drazen Adamovic, Ozren Perse, Paolo Papi, Pierluigi Moseneder Frajria, Victor G. Kac","submitted_at":"2016-02-15T14:11:58Z","abstract_excerpt":"We find all values of $k\\in \\mathbb C$, for which the embedding of the maximal affine vertex algebra in a simple minimal W-algebra $W_k(\\mathfrak g,\\theta)$ is conformal, where $\\mathfrak g$ is a basic simple Lie superalgebra and $-\\theta$ its minimal root. In particular, it turns out that if $W_k(\\mathfrak g,\\theta)$ does not collapse to its affine part, then the possible values of these $k$ are either $-\\frac{2}{3} h^\\vee$ or $-\\frac{h^\\vee-1}{2}$, where $h^\\vee$ is the dual Coxeter number of $\\mathfrak g$ for the normalization $(\\theta,\\theta)=2$. As an application of our results, we presen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04687","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}