Details
| Original language | English |
|---|---|
| Pages (from-to) | 313-329 |
| Number of pages | 17 |
| Journal | Journal of noncommutative geometry |
| Volume | 4 |
| Issue number | 3 |
| Publication status | Published - 26 Jul 2010 |
Abstract
Can Boutet de Monvel's algebra on a compact manifold with boundary be obtained as the algebra ψ0(G) of pseudo differential operators on some Lie groupoid G? If it could, the kernel 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 I isomorphic to G. In fact, we prove first that G ≃ψ⊗ Κwith the Cz.ast;-algebra ψ generated by the zero order pseudo differential operators on the boundary and the algebra Κof compact operators. As both ψ Κ ⊗ Κ are extensions of C (S*Y) ψ ⊗ Κ by Κ(S*Y is the co-sphere bundle over the boundary) we infer from a theorem by Voiculescu that both are isomorphic. theory.
Keywords
- Boundary value problems on manifolds, Extension, Groupoids, Index theory, KK-theory
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
- Mathematics(all)
- Mathematical Physics
- Mathematics(all)
- Geometry and Topology
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In: Journal of noncommutative geometry, Vol. 4, No. 3, 26.07.2010, p. 313-329.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Boutet de Monvel's calculus and groupoids i
AU - Aastrup, Johannes
AU - Melo, Severino T.
AU - Monthubert, Bertrand
AU - Schrohe, Elmar
N1 - Copyright: Copyright 2010 Elsevier B.V., All rights reserved.
PY - 2010/7/26
Y1 - 2010/7/26
N2 - Can Boutet de Monvel's algebra on a compact manifold with boundary be obtained as the algebra ψ0(G) of pseudo differential operators on some Lie groupoid G? If it could, the kernel 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 I isomorphic to G. In fact, we prove first that G ≃ψ⊗ Κwith the Cz.ast;-algebra ψ generated by the zero order pseudo differential operators on the boundary and the algebra Κof compact operators. As both ψ Κ ⊗ Κ are extensions of C (S*Y) ψ ⊗ Κ by Κ(S*Y is the co-sphere bundle over the boundary) we infer from a theorem by Voiculescu that both are isomorphic. theory.
AB - Can Boutet de Monvel's algebra on a compact manifold with boundary be obtained as the algebra ψ0(G) of pseudo differential operators on some Lie groupoid G? If it could, the kernel 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 I isomorphic to G. In fact, we prove first that G ≃ψ⊗ Κwith the Cz.ast;-algebra ψ generated by the zero order pseudo differential operators on the boundary and the algebra Κof compact operators. As both ψ Κ ⊗ Κ are extensions of C (S*Y) ψ ⊗ Κ by Κ(S*Y is the co-sphere bundle over the boundary) we infer from a theorem by Voiculescu that both are isomorphic. theory.
KW - Boundary value problems on manifolds
KW - Extension
KW - Groupoids
KW - Index theory
KW - KK-theory
UR - http://www.scopus.com/inward/record.url?scp=77955621254&partnerID=8YFLogxK
U2 - 10.4171/JNCG/57
DO - 10.4171/JNCG/57
M3 - Article
AN - SCOPUS:77955621254
VL - 4
SP - 313
EP - 329
JO - Journal of noncommutative geometry
JF - Journal of noncommutative geometry
SN - 1661-6952
IS - 3
ER -