SIGMA 5 (2009), 061, 13 pages arXiv:0906.2554
Contribution to the Special Issue “Élie Cartan and Differential Geometry”
Cartan Connections and Lie Algebroids
Department of Mathematical Physics and Astronomy, Ghent University, Krijgslaan 281, B-9000 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
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].
adjoint tractor bundle; algebroid connection; algebroid representation; Cartan connection; Cartan geometry; Lie algebroid; tractor calculus.
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Geometric structures as deformed infinitesimal symmetries,
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Infinitesimal automorphisms and deformations of parabolic geometries,
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- Cap A., Gover A.R.,
Tractor calculi for parabolic geometries,
Trans. Amer. Math. Soc. 354 (2001), 1511-1548.
- 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, Springer-Verlag, New York, 1997.