Lie rackoids

2015/11/10 by Camille Laurent-Gengoux, Laurent-Gengoux, Camille, Friedrich Wagemann +1
Mathematics · #20L05 #22E65 #58B25 #58H05 #Differential Geometry (math.DG) #FOS: Mathematics #Quantum Algebra (math.QA) #math.DG #math.QA #msc:20L05 #msc:22E65 #msc:58B25 #msc:58H05

paper · pdf · doi:10.48550/arxiv.1511.03018

23 pages, no figures

arxiv created 2015/11/10 · arxiv updated 2015/11/11

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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