{"paper":{"title":"Lie Algebroids Associated to Poisson Actions","license":"","headline":"","cross_cats":["dg-ga","math.DG","math.QA"],"primary_cat":"q-alg","authors_text":"Jiang-Hua Lu","submitted_at":"1995-03-08T23:37:40Z","abstract_excerpt":"This work is motivated by a result of Drinfeld on Poisson homogeneous spaces. For each Poisson manifold $P$ with a Poisson action by a Poisson Lie group $G$, we describe a Lie algebroid structure on the direct sum vector bundle $P \\times {\\frak g} \\oplus T^*P$, where ${\\frak g}$ is the Lie algebra of $G$. It is built out of the transformation Lie algebroid $P \\times {\\frak g}$ and the cotangent bundle Lie algebroid $T^*P$ together with a pair of representations of them on each other. When the action of $G$ on $P$ is transitive, the kernel of the anchor map of this Lie algebroid gives a Lie alg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-alg/9503003","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"}