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Abstract: A Dirac structure on a vector bundle V is a maximal isotropic subbundle E ofthe direct sum of V with its dual. We show how to associate to any Diracstructure a Dixmier-Douady bundle A, that is, a Z-2Z-graded bundle ofC*-algebras with typical fiber the compact operators on a Hilbert space. Theconstruction has good functorial properties, relative to Morita morphisms ofDixmier-Douady bundles. As applications, we show that the `spin- Dixmier-Douadybundle over a compact, connected Lie group as constructed by Atiyah-Segal ismultiplicative, and we obtain a canonical `twisted Spin-c-structure- on spaceswith group valued moment maps.



Autor: A. Alekseev, E. Meinrenken

Fuente: https://arxiv.org/



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