{"paper":{"title":"Dirac structures of omni-Lie algebroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Yunhe Sheng, Zhangju Liu, Zhuo Chen","submitted_at":"2008-02-26T14:45:32Z","abstract_excerpt":"Omni-Lie algebroids are generalizations of Alan Weinstein's omni-Lie algebras. A Dirac structure in an omni-Lie algebroid $\\dev E\\oplus \\jet E$ is necessarily a Lie algebroid together with a representation on $E$. We study the geometry underlying these Dirac structures in the light of reduction theory. In particular, we prove that there is a one-to-one correspondence between reducible Dirac structures and projective Lie algebroids in $\\huaT=TM\\oplus E$; we establish the relation between the normalizer $N_{L}$ of a reducible Dirac structure $L$ and the derivation algebra $\\Der(\\pomnib (L))$ of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.3819","kind":"arxiv","version":3},"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"}