{"paper":{"title":"Special symplectic Lie groups and hypersymplectic Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.MP","math.QA","math.SG"],"primary_cat":"math-ph","authors_text":"Chengming Bai, Xiang Ni","submitted_at":"2010-10-15T13:32:24Z","abstract_excerpt":"A special symplectic Lie group is a triple $(G,\\omega,\\nabla)$ such that $G$ is a finite-dimensional real Lie group and $\\omega$ is a left invariant symplectic form on $G$ which is parallel with respect to a left invariant affine structure $\\nabla$. In this paper starting from a special symplectic Lie group we show how to ``deform\" the standard Lie group structure on the (co)tangent bundle through the left invariant affine structure $\\nabla$ such that the resulting Lie group admits families of left invariant hypersymplectic structures and thus becomes a hypersymplectic Lie group. We consider t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3160","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"}