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Keller, Frank; Waldmann, Stefan

Deformation theory of Courant algebroids via the Rothstein algebra. (English) Zbl 1315.53103

J. Pure Appl. Algebra 219, No. 8, 3391-3426 (2015).
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.
Reviewer: Angela Gammella-Mathieu (Metz)

Cited in 2 Reviews
Cited in 14 Documents

MSC:

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

Keywords:

deformation quantization; Courant algebroids; graded Poisson algebras; Fedosov method; Lie-Rinehard pair
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\textit{F. Keller} and \textit{S. Waldmann}, J. Pure Appl. Algebra 219, No. 8, 3391--3426 (2015; Zbl 1315.53103)
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