{"paper":{"title":"Almost K\\\"ahler structures on four dimensional unimodular Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Adriano Tomassini, Tian-Jun Li","submitted_at":"2012-03-20T07:25:05Z","abstract_excerpt":"Let $J$ be an almost complex structure on a 4-dimensional and unimodular Lie algebra $\\mathfrak{g}$. We show that there exists a symplectic form taming $J$ if and only if there is a symplectic form compatible with $J$. We also introduce groups $H^+_J(\\mathfrak{g})$ and $H^-_J(\\mathfrak{g})$ as the subgroups of the Chevalley-Eilenberg cohomology classes which can be represented by $J$-invariant, respectively $J$-anti-invariant, 2-forms on $\\mathfrak{g}$. and we prove a cohomological $J-$decomposition theorem following \\cite{DLZ}: $H^2(\\mathfrak{g})=H^+_J(\\mathfrak{g})\\oplus H^-_J(\\mathfrak{g})$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4331","kind":"arxiv","version":1},"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"}