Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 9 (2013), 014, 8 pages      arXiv:1212.0559      http://dx.doi.org/10.3842/SIGMA.2013.014
Contribution to the Special Issue “Symmetries of Differential Equations: Frames, Invariants and Applications”

Courant Algebroids. A Short History

Yvette Kosmann-Schwarzbach
Centre de Mathématiques Laurent Schwartz, École Polytechnique, F-91128 Palaiseau, France

Received December 03, 2012, in final form February 14, 2013; Published online February 19, 2013

Abstract
The search for a geometric interpretation of the constrained brackets of Dirac led to the definition of the Courant bracket. The search for the right notion of a ''double'' for Lie bialgebroids led to the definition of Courant algebroids. We recount the emergence of these concepts.

Key words: Courant algebroid; Dorfman bracket; Lie algebroid; Lie bialgebroid; generalized geometry; Dirac structure; Loday algebra; Leibniz algebra; derived bracket.

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