{"paper":{"title":"The Pontryagin Class for Pre-Courant Algebroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"Xiaomeng Xu, Yunhe Sheng, Zhangju Liu","submitted_at":"2012-05-26T17:10:51Z","abstract_excerpt":"In this paper, we show that the Jacobiator $J$ of a pre-Courant algebroid is closed naturally. The corresponding equivalence class $[J^\\flat]$ is defined as the Pontryagin class, which is the obstruction of a pre-Courant algebroid to be deformed into a Courant algebroid. We construct a Leibniz 2-algebra and a Lie 2-algebra associated to a pre-Courant algebroid and prove that these algebraic structures are isomorphic under deformations. Finally, we introduce the twisted action of a Lie algebra on a manifold to give more examples of pre-Courant algebroids, which include the Cartan geometry."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5898","kind":"arxiv","version":2},"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"}