Journal of Lie Theory 18 (2008), No. 1, 093--123
Copyright Heldermann Verlag 2008
Transvection and Differential Invariants of Parametrized Curves
Gloria Marí Beffa
Mathematics Department, University of Wisconsin, Madison, WI 53706, U.S.A.
maribeff@math.wisc.edu
Jan A. Sanders
Mathematics Department, Vrije Universiteit, 1081 HV Amsterdam, Netherlands
jansa@cs.vu.nl
We describe an sl2 representation in the space of differential invariants of parametrized curves in homogeneous spaces. The representation is described by three operators, one of them being the total derivative D. We use this representation to find a basis for the space of differential invariants of curves in a complement of the image of D, and so generated by transvection. These are natural representatives of first cohomology classes in the invariant bicomplex. We describe algorithms to find these basis and study most well-known geometries.
Keywords: Transvectant, differential invariants, curves, affine manifold, symmetric manifold.
MSC: 13A50, 53A55
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