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Article Dans Une Revue Journal of Geometry and Physics Année : 2020

Cartan Connections and Atiyah Lie Algebroids

Résumé

This work extends previous developments carried out by some of the authors on Ehresmann connections on Atiyah Lie algebroids. In this paper, we study Cartan connections in a framework relying on two Atiyah Lie algebroids based on a $H$-principal fiber bundle $\mathcal{P}$ and its associated $G$-principal fiber bundle $\mathcal{Q} := \mathcal{P} \times_H G$, where $H \subset G$ defines the model for a Cartan geometry. The first main result of this study is a commutative and exact diagram relating these two Atiyah Lie algebroids, which allows to completely characterize Cartan connections on $\mathcal{P}$. Furthermore, in the context of gravity and mixed anomalies, our construction answers a long standing mathematical question about the correct geometrico-algebraic setting in which to combine inner gauge transformations and infinitesimal diffeomorphisms.
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Dates et versions

hal-02097864 , version 1 (21-07-2022)

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Paternité - Pas d'utilisation commerciale

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Jérémy Attard, Jordan François, Serge Lazzarini, Thierry Masson. Cartan Connections and Atiyah Lie Algebroids. Journal of Geometry and Physics, 2020, 148, pp.103541. ⟨10.1016/j.geomphys.2019.103541⟩. ⟨hal-02097864⟩
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