{"paper":{"title":"Weak Mirror Symmetry of Complex Symplectic Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Gabriela P. Ovando, Richard Cleyton, Yat Sun Poon","submitted_at":"2010-04-19T18:03:39Z","abstract_excerpt":"A complex symplectic structure on a Lie algebra $\\lie h$ is an integrable complex structure $J$ with a closed non-degenerate $(2,0)$-form. It is determined by $J$ and the real part $\\Omega$ of the $(2,0)$-form. Suppose that $\\lie h$ is a semi-direct product $\\lie g\\ltimes V$, and both $\\lie g$ and $V$ are Lagrangian with respect to $\\Omega$ and totally real with respect to $J$. This note shows that $\\lie g\\ltimes V$ is its own weak mirror image in the sense that the associated differential Gerstenhaber algebras controlling the extended deformations of $\\Omega$ and $J$ are isomorphic. The geome"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3264","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"}