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Induced C*-Complexes in Metaplectic Geometry

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Abstract

For a symplectic manifold admitting a metaplectic structure and for a Kuiper map, we construct a complex of differential operators acting on exterior differential forms with values in the dual of Kostant’s symplectic spinor bundle. Defining a Hilbert C*-structure on this bundle for a suitable C*-algebra, we obtain an elliptic C*-complex in the sense of Mishchenko–Fomenko. Its cohomology groups appear to be finitely generated projective Hilbert C*-modules. The paper can serve as a guide for handling differential complexes and PDEs on Hilbert bundles.

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  1. Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic

    Svatopluk Krýsl

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Correspondence to Svatopluk Krýsl.

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Communicated by C. Schweigert

The author thanks for financial supports from the founding No. 17-01171S granted by the Czech Science Foundation. We thank to the anonymous reviewer for his comments and suggestions.

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Krýsl, S. Induced C*-Complexes in Metaplectic Geometry. Commun. Math. Phys. 365, 61–91 (2019). https://doi.org/10.1007/s00220-018-3275-9

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