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  • Volume 3 (2013)
  • no. 1
  • Talk no. 3
no. 1
Rational Invariants of a Group Action
Evelyne Hubert1
1 INRIA Méditerranée, France
Les cours du CIRM, Volume 3 (2013) no. 1, Talk no. 3, 10 p.
  • Abstract

This article is based on an introductory lecture delivered at the Journée Nationales de Calcul Formel that took place at the Centre International de Recherche en Mathématiques (2013) in Marseille. We introduce basic notions on algebraic group actions and their invariants. Based on geometric consideration, we present algebraic constructions for a generating set of rational invariants. http://hal.inria.fr/hal-00839283

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Published online: 2013-09-22
DOI: 10.5802/ccirm.19
Author's affiliations:
Evelyne Hubert 1

1 INRIA Méditerranée, France
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     author = {Evelyne Hubert},
     title = {Rational {Invariants} of a {Group} {Action}},
     journal = {Les cours du CIRM},
     note = {talk:3},
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     volume = {3},
     number = {1},
     year = {2013},
     doi = {10.5802/ccirm.19},
     language = {en},
     url = {https://ccirm.centre-mersenne.org/articles/10.5802/ccirm.19/}
}
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Evelyne Hubert. Rational Invariants of a Group Action. Les cours du CIRM, Volume 3 (2013) no. 1, Talk no. 3, 10 p. doi : 10.5802/ccirm.19. https://ccirm.centre-mersenne.org/articles/10.5802/ccirm.19/
  • References
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[DK02] H. Derksen and G. Kemper. Computational invariant theory. Invariant Theory and Algebraic Transformation Groups I. Springer-Verlag, Berlin, 2002. Encyclopaedia of Math. Sc., 130.

[FO99] M. Fels and P. J. Olver. Moving coframes. II. Regularization and theoretical foundations. Acta Appl. Math., 55(2):127–208, 1999.

[HK07a] E. Hubert and I. A. Kogan. Rational invariants of a group action. Construction and rewriting. Journal of Symbolic Computation, 42(1-2):203–217, 2007.

[HK07b] E. Hubert and I. A. Kogan. Smooth and algebraic invariants of a group action. Local and global constructions. Foundations of Computational Mathematics, 7(4), 2007.

[HL12] E. Hubert and G. Labahn. Rational invariants of scalings from Hermite normal forms. In Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation, ISSAC ’12, pages 219–226, New York, NY, USA, 2012. ACM.

[HL13] E. Hubert and G. Labahn. Scaling invariants and symmetry reduction of dynamical systems. Foundations of Computational Mathematics, 2013.

[Hub09] E. Hubert. Differential invariants of a Lie group action: syzygies on a generating set. Journal of Symbolic Computation, 44(3):382–416, 2009.

[Hub12] E. Hubert. Algebraic and differential invariants. In F. Cucker, T. Krick, A. Pinkus, and A. Szanto, editors, Foundations of computational mathematics, Budapest 2011, number 403 in London Mathematical Society Lecture Note Series. Cambrige University Press, 2012.

[Kem07] G. Kemper. The computation of invariant fields and a new proof of a theorem by Rosenlicht. Transformation Groups, 12:657–670, 2007.

[MQB99] J. Müller-Quade and T. Beth. Calculating generators for invariant fields of linear algebraic groups. In Applied algebra, algebraic algorithms and error-correcting codes (Honolulu, HI, 1999), volume 1719 of Lecture Notes in Computer Science, pages 392–403. Springer, Berlin, 1999.

[PV94] V. L. Popov and E. B. Vinberg. Invariant theory. In A. N. Parshin and I. R. Shafarevich, editors, Algebraic geometry. IV, volume 55 of Encyclopaedia of Mathematical Sciences, pages 122–278. Springer-Verlag, Berlin, 1994.

[Ros56] M. Rosenlicht. Some basic theorems on algebraic groups. American Journal of Mathematics, 78:401–443, 1956.

[Stu93] B. Sturmfels. Algorithms in invariant theory. Texts and Monographs in Symbolic Computation. Springer-Verlag, Vienna, 1993.

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