XXXIV Workshop on Geometric Methods in Physics | 28.06-4.07.2015 |

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## Andreas Deser## Star products on graded manifolds and deformations of Courant algebroids from string theoryDeformations of Courant algebroids are of interest in both, string theory and mathematics. It was realized by Roytenberg, that Lie bialgebroids and their associated Courant algebroids can be characterized by a homological vector field on the cotangent bundle of the parity reversed version of the underlying Lie algebroid. This lead to the introduction of the Drinfel'd double of a Lie bialgebroid. In a similar way, we show that the so-called C-bracket, a bi-linear operation governing the gauge algebra of double field theory, can be characterized by the Poisson structure on the Drinfel'd double of the underlying Lie-bialgebroid. Using this result, we are able to apply a graded version of the Moyal-Weyl star product to compute the first order deformation of the C-bracket. Remarkably, these coincide with the first order correction in the string coupling parameter found recently in string theory. |

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