Lie rackoids integrating Courant algebroids

Laurent-Gengoux, Camille; Wagemann, Friedrich

doi:10.1007/s10455-019-09697-2

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Lie rackoids integrating Courant algebroids

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Laurent-Gengoux, Camille
Max Planck Institute for Mathematics, Max Planck Society;

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Wagemann, Friedrich
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s10455-019-09697-2
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Citation

Laurent-Gengoux, C., & Wagemann, F. (2020). Lie rackoids integrating Courant algebroids. Annals of Global Analysis and Geometry, 57(2), 225-256. doi:10.1007/s10455-019-09697-2.

Cite as: https://hdl.handle.net/21.11116/0000-0005-EE1A-3

Abstract

We construct an infinite dimensional Lie rackoid Y which hosts an integration of the standard Courant algebroid. As a set, Y = C $\infty$ ([0, 1], T * M) for a compact manifold M. The rackoid product is by automorphisms of the Dorfman bracket. The first part of the article is a study of the Lie rackoid Y and its tangent Leibniz algebroid a quotient of which is the standard Courant
algebroid. In a second part, we study the equivalence relation related to the quotient on the rackoid level and restrict then to an integrable Dirac structure. We show how our integrating object contains the corresponding integrating Weinstein Lie groupoid in the case where the Dirac structure is given by a Poisson structure.