{"paper":{"title":"Holomorphic current groups -- Structure and Orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CV","math.DG","math.MP"],"primary_cat":"math.AT","authors_text":"Friedrich Wagemann, Martin Laubinger","submitted_at":"2014-08-18T12:09:26Z","abstract_excerpt":"Let K be a finite-dimensional, 1-connected complex Lie group, and let \\Sigma_k=\\Sigma - {p_1,\\ldots,p_k\\} be a compact connected Riemann surface \\Sigma, from which we have extracted k > 0 distinct points. We study in this article the regular Frechet-Lie group O(\\Sigma_k,K) of holomorphic maps from \\Sigma_k to K and its central extension \\widehat{O(\\Sigma_k,K)}. We feature especially the automorphism groups of these Lie groups as well as the coadjoint orbits of \\widehat{O(\\Sigma_k,K)} which we link to flat K-bundles on \\Sigma_k."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3990","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"}