2006/11/11 by Johannes Aastrup, Aastrup, Johannes, Severino T. Melo +5
Mathematics · #35S05 #58B34 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #math.KT #math.OA #msc:35S05 #msc:58B34
paper · pdf · doi:10.48550/arxiv.math/0611336
17 pages
arxiv created 2006/11/11 · openalex publication_date 2006/11/11 · arxiv updated 2016/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Can Boutet de Monvel's algebra on a compact manifold with boundary be obtained as the algebra Ψ0(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 \mathcal G≃Ψ⊗\mathcal K with the C^*-algebra Ψ generated by the zero order pseudodifferential operators on the boundary and the algebra \mathcal K of compact operators. As both Ψ⊗ \mathcal K and \mathcal I are extensions of C(S^*Y)⊗ K by K (S^*Y is the co-sphere bundle over the boundary) we infer from a theorem by Voiculescu that both are isomorphic.