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

Evelyne Hubert 1 Irina Kogan 2
1 CRISAM - Inria Sophia Antipolis - Méditerranée
2 Department of mathematics [North Carolina]
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.
Keywords : Groebner basis rational and algebraic invariants smooth and differential invariants algebraic and Lie group actions cross-section moving frame method Groebner basis.
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https://hal.inria.fr/inria-00198857
Contributor : Evelyne Hubert <>
Submitted on : Tuesday, December 18, 2007 - 9:30:53 AM
Last modification on : Wednesday, August 21, 2019 - 10:38:02 AM

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Evelyne Hubert, Irina Kogan. Smooth and Algebraic Invariants of a Group Action: Local and Global Constructions. Foundations of Computational Mathematics, Springer Verlag, 2007, 7 (4), pp.455-493. ⟨10.1007/s10208-006-0219-0⟩. ⟨inria-00198857⟩

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