Hodge theory for elliptic complexes over unital C^*-algebras |
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Authors: | Svatopluk Krýsl |
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Affiliation: | 1. Faculty of Mathematics and Physics, Charles University in Prague, Praha 8, Karlin, Czech Republic
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Abstract: | For a unital $C^{*}$ -algebra $A$ , we prove that the cohomology groups of $A$ -elliptic complexes of pseudodifferential operators in finitely generated projective $A$ -Hilbert bundles over compact manifolds are finitely generated $A$ -modules and Banach spaces provided the images of certain extensions of the so-called associated Laplacians are closed. We also prove that under this condition, the cohomology groups are isomorphic to the kernels of the associated Laplacians. This establishes a Hodge theory for these structures. |
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