Rational, Replacement, and Local Invariants of a Group Action

Evelyne Hubert (1) , Irina Kogan (2)

1 CAFE - Computer algebra and functional equations
2 Department of mathematics [North Carolina]

The paper presents a new algorithmic construction of a finite generating set of rational invariants for the rational action of an algebraic group on the affine space. The construction provides an algebraic counterpart of the moving frame method in differential geometry. The generating set of rational invariants appears as the coefficients of a Groebner basis, reduction with respect to which allows to express a rational invariant in terms of the generators. The replacement invariants, introduced in the paper, are tuples of algebraic functions of the rational invariants. Any invariant, whether rational, algebraic or local, can be can be rewritten terms of replacement invariants by a simple substitution.

Mots clés: invariants rationels et algébriques; invariants differentiels; action d'un groupe algébriques; bases de Groebner; méthode du repère mobile

Domaines: Mathématiques générales [math.GM]; Algèbre commutative [math.AC]; Géométrie différentielle [math.DG]

Evelyne Hubert, Irina Kogan. Rational, Replacement, and Local Invariants of a Group Action. 2005. ⟨hal-00008497⟩