12 Citations (Scopus)

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 H3 DR(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 - Jan 1 2013

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Characteristic Classes
Quadratic Algebras
Cohomology
Lie Algebra
Invariant
Class
Form

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Cite this

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title = "On regular Courant algebroids",
abstract = "For any regular Courant algebroid, we construct a characteristic class {\`a} 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 H3 DR(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.",
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year = "2013",
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language = "English (US)",
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On regular Courant algebroids. / Chen, Zhuo; Stienon, Mathieu Philippe; Xu, Ping.

In: Journal of Symplectic Geometry, Vol. 11, No. 1, 01.01.2013, p. 1-24.

Research output: Contribution to journalArticle

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T1 - On regular Courant algebroids

AU - Chen, Zhuo

AU - Stienon, Mathieu Philippe

AU - Xu, Ping

PY - 2013/1/1

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N2 - 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 H3 DR(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.

AB - 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 H3 DR(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.

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