Hodge theory for elliptic complexes over unital C*-algebras

Abstract

For a unital -algebra , we prove that the cohomology groups of -elliptic complexes of pseudodifferential operators in finitely generated projective -Hilbert bundles over compact manifolds are finitely generated -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.

Keywords

• Hodge theory
• Elliptic complexes
• A-Hilbert bundles