On regular Courant algebroids

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Abstract

For any regular Courant algebroid, we construct a characteristic class à la Chern-Weil. This intrinsic invariant of the Courant algebroid is a degree-3 class in its naive cohomology. When the Courant algebroid is exact, it reduces to the Ševera class in H3DR(M). On the other hand, when the Courant algebroid is a quadratic Lie algebra g, it coincides with the class of the Cartan 3-form in H3(g). We also give a complete classification of regular Courant algebroids and discuss its relation to the characteristic class.

Original languageEnglish (US)
Pages (from-to)1-24
Number of pages24
JournalJournal of Symplectic Geometry
Volume11
Issue number1
DOIs
StatePublished - Mar 2013

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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