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Smooth and Algebraic Invariants of a Group Action: Local and Global Constructions

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Abstract

We provide an algebraic formulation of the moving frame method for constructing local smooth invariants on a manifold under an action of a Lie group. This formulation gives rise to algorithms for constructing rational and replacement invariants. The latter are algebraic over the field of rational invariants and play a role analogous to Cartan's normalized invariants in the smooth theory. The algebraic algorithms can be used for computing fundamental sets of differential invariants.

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Authors and Affiliations

  1. INRIA Sophia Antipolis, 2004 route des lucioles, 06902 Sophia Antipolis, France

    Evelyne Hubert

  2. Department of Mathematics, North Carolina State University, 245 Harrelson Hall, Campus Box 8205, Raleigh, NC 27695, USA

    Irina A. Kogan

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  1. Evelyne Hubert
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  2. Irina A. Kogan
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Hubert, E., Kogan, I. Smooth and Algebraic Invariants of a Group Action: Local and Global Constructions. Found Comput Math 7, 455–493 (2007). https://doi.org/10.1007/s10208-006-0219-0

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  • DOI: https://doi.org/10.1007/s10208-006-0219-0

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