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arXiv · 1511.03018

Lie rackoids

Camille Laurent-Gengoux·Friedrich Wagemann
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Abstract

We define a new differential geometric structure, called Lie rackoid. It relates to Leibniz algebroids exactly as Lie groupoids relate to Lie algebroids. Its main ingredient is a selfdistributive product on the manifold of bisections of a smooth precategory. We show that the tangent algebroid of a Lie rackoid is a Leibniz algebroid and that Lie groupoids gives rise via conjugation to a Lie rackoid. Our main objective are large classes of examples, including a Lie rackoid integrating the Dorfman bracket without the cocycle term of the standard Courant algebroid.

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Camille Laurent-Gengoux, Friedrich Wagemann. 2015-11-10. Lie rackoids. https://arxiv.org/abs/1511.03018

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