{"paper":{"title":"Atiyah classes and dg-Lie algebroids for matched pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Panagiotis Batakidis, Yannick Voglaire","submitted_at":"2016-01-23T09:03:34Z","abstract_excerpt":"For every Lie pair $(L,A)$ of algebroids we construct a dg-manifold structure on the $\\mathbb{Z}$-graded manifold $\\mathcal M=L[1]\\oplus L/A$ such that the inclusion $\\iota: A[1] \\to \\mathcal M$ and the projection $p:\\mathcal M\\to L[1]$ are morphisms of dg-manifolds. The vertical tangent bundle $T^p\\mathcal M$ then inherits a structure of dg-Lie algebroid over $\\mathcal M$. When the Lie pair comes from a matched pair of Lie algebroids, we show that the inclusion $\\iota$ induces a quasi-isomorphism that sends the Atiyah class of this dg-Lie algebroid to the Atiyah class of the Lie pair. We also"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06254","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"}