{"paper":{"title":"Boutet de Monvel's Calculus and Groupoids I","license":"","headline":"","cross_cats":["math.OA"],"primary_cat":"math.KT","authors_text":"Bertrand Monthubert (IMT), Elmar Schrohe (Institut F\\\"ur Analysis), Johannes Aastrup (Institut F\\\"ur Analysis), Severino T. Melo (Instituto De Matem\\'atica E Estat\\'istica)","submitted_at":"2006-11-11T21:22:52Z","abstract_excerpt":"Can Boutet de Monvel's algebra on a compact manifold with boundary be obtained as the algebra $\\Psi^0(G)$ of pseudodifferential operators on some Lie groupoid $G$? If it could, the kernel ${\\mathcal G}$ of the principal symbol homomorphism would be isomorphic to the groupoid {$C^*$-algebra} $C^*(G)$. While the answer to the above question remains open, we exhibit in this paper a groupoid $G$ such that $C^*(G)$ possesses an ideal ${\\mathcal I}$ isomorphic to ${\\mathcal G}$. %ES, the kernel of the principal symbol homomorphism on Boutet de Monvel's algebra. In fact, we prove first that ${\\mathca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611336","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"}