{"paper":{"title":"Coclosed $G_2$-structures inducing nilsolitons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Anna Fino, Leonardo Bagaglini, Marisa Fern\\'andez","submitted_at":"2016-11-16T13:11:48Z","abstract_excerpt":"We show obstructions to the existence of a coclosed $G_2$-structure on a Lie algebra $\\mathfrak g$ of dimension seven with non-trivial center. In particular, we prove that if there exist a Lie algebra epimorphism from $\\mathfrak g$ to a six-dimensional Lie algebra $\\mathfrak h$, with kernel contained in the center of $\\mathfrak g$, then any coclosed $G_2$-structure on $\\mathfrak g$ induces a closed and stable three form on $\\mathfrak h$ that defines an almost complex structure on $\\mathfrak h$. As a consequence, we obtain a classification of the 2-step nilpotent Lie algebras which carry coclos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05264","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"}