Elliptic complexes over C∗-algebras of compact operators
| Autor: | Svatopluk Krýsl |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Hilbert manifold Hodge theory 010102 general mathematics Hilbert's fourteenth problem General Physics and Astronomy Compact operator 01 natural sciences Compact operator on Hilbert space Cohomology Algebra 0103 physical sciences Elliptic complex Projective Hilbert space 010307 mathematical physics Geometry and Topology 0101 mathematics Mathematical Physics Mathematics |
| Zdroj: | Journal of Geometry and Physics. 101:27-37 |
| ISSN: | 0393-0440 |
| DOI: | 10.1016/j.geomphys.2015.12.001 |
| Popis: | For a C ∗ -algebra A of compact operators and a compact manifold M , we prove that the Hodge theory holds for A -elliptic complexes of pseudodifferential operators acting on smooth sections of finitely generated projective A -Hilbert bundles over M . For these C ∗ -algebras and manifolds, we get a topological isomorphism between the cohomology groups of an A -elliptic complex and the space of harmonic elements of the complex. Consequently, the cohomology groups appear to be finitely generated projective C ∗ -Hilbert modules and especially, Banach spaces. We also prove that in the category of Hilbert A -modules and continuous adjointable Hilbert A -module homomorphisms, the property of a complex of being self-adjoint parametrix possessing characterizes the complexes of Hodge type. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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