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Dirac structures and Dixmier-Douady bundles | | A. Alekseev
; E. Meinrenken
; | | Date: |
7 Jul 2009 | | Abstract: | A Dirac structure on a vector bundle V is a maximal isotropic subbundle E of
the direct sum of V with its dual. We show how to associate to any Dirac
structure a Dixmier-Douady bundle A, that is, a Z/2Z-graded bundle of
C*-algebras with typical fiber the compact operators on a Hilbert space. The
construction has good functorial properties, relative to Morita morphisms of
Dixmier-Douady bundles. As applications, we show that the ’spin’ Dixmier-Douady
bundle over a compact, connected Lie group (as constructed by Atiyah-Segal) is
multiplicative, and we obtain a canonical ’twisted Spin-c-structure’ on spaces
with group valued moment maps. | | Source: | arXiv, 0907.1257 | | Services: | Forum | Review | PDF | Favorites | |
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