Automorphismes forts des algébroïdes de Courant réguliers

Abstract : Courant algebroids have been introduced by T. J. Courant in his PhD thesis concerning the integrability of Dirac structures. They have become important objects in differential geometry since the seminal work of Z.-J. Liu, A. Weinstein and P. Xu on Lie bialgebroids. They play an increasing role in theoretical physics as well as inmathematics. In this thesis, we are interested by describing strong automorphisms of a regular Courant algebroid. In a first part, we review Lie algebroids. In a second part, we study Courant algebroids. In a third part, after introducing the notion of dissection, we compute the automorphism group of a regular Courant algebroid with respect to a dissection of it, and then compute the Lie algebra of infinitesimal automorphisms with respect to this dissection. From this work appeared new symmetries that could be useful in theoretical physics.
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Benjamin Coueraud. Automorphismes forts des algébroïdes de Courant réguliers. Géométrie algébrique [math.AG]. Université d'Angers, 2015. Français. ⟨NNT : 2015ANGE0017⟩. ⟨tel-01278988⟩

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