
SIGMA 5 (2009), 061, 13 pages arXiv:0906.2554
https://doi.org/10.3842/SIGMA.2009.061
Contribution to the Special Issue “Élie Cartan and Differential Geometry”
Cartan Connections and Lie Algebroids
Michael Crampin
Department of Mathematical Physics and Astronomy, Ghent University, Krijgslaan 281, B9000 Gent, Belgium
Address for correspondence: 65 Mount Pleasant, Aspley Guise, Beds MK17 8JX, UK
Received March 23, 2009, in final form June 07, 2009; Published online June 14, 2009
Abstract
This paper is a study of the relationship
between two constructions associated with Cartan geometries, both of
which involve Lie algebroids: the Cartan algebroid, due to
[Blaom A.D., Trans. Amer. Math. Soc. 358 (2006), 3651–3671], and tractor calculus [Cap A., Gover A.R., Trans. Amer. Math. Soc. 354 (2001), 1511–1548].
Key words:
adjoint tractor bundle; algebroid connection; algebroid representation; Cartan connection; Cartan geometry; Lie algebroid; tractor calculus.
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References
 Blaom A.D.,
Geometric structures as deformed infinitesimal symmetries,
Trans. Amer. Math. Soc. 358 (2006), 36513671,
math.DG/0404313.
 Cap A.,
Infinitesimal automorphisms and deformations of parabolic geometries,
J. Eur. Math. Soc. (JEMS) 10 (2008), 415437,
math.DG/0508535.
 Cap A., Gover A.R.,
Tractor calculi for parabolic geometries,
Trans. Amer. Math. Soc. 354 (2001), 15111548.
 Sharpe R.W.,
Differential geometry. Cartan's generalization of Klein's Erlangen program, with a foreword by S.S. Chern, Graduate Texts in Mathematics, Vol. 166, SpringerVerlag, New York, 1997.

