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Deformation theory of Courant algebroids via the Rothstein algebra. (English) Zbl 1315.53103
This paper studies two kind of deformations for Courant algebroids. Let us recall that a Courant algebroid is a vector bundle with a definite non-degenerate fiber metric. This notion has been extensively developed in the literature. In this work, the authors introduce a notion of Courant algebroids in a purely algebraic framework. They then study the corresponding deformation. Fedosov’s method is used. Finally, it is showed how a Lie-Rinehart pair can be viewed as a Courant algebroid.

MSC:
53D55 Deformation quantization, star products
53D15 Almost contact and almost symplectic manifolds
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