Centre de diffusion de revues académiques mathématiques

 
 
 
 

Les cours du CIRM

Table des matières de ce fascicule | Article précédent
Evelyne Hubert
Rational Invariants of a Group Action
Les cours du CIRM, 3 no. 1: Journées Nationales de Calcul Formel (2013), Exp. No. 3, 10 p., doi: 10.5802/ccirm.19
Article PDF

Résumé - 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

Bibliographie

[Der99] H. Derksen. Computation of invariants for reductive groups. Adv. Math., 141(2):366–384, 1999.  MR 1671758 |  Zbl 0927.13007
[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.  MR 1918599 |  Zbl 1011.13003
[FO99] M. Fels and P. J. Olver. Moving coframes. II. Regularization and theoretical foundations. Acta Appl. Math., 55(2):127–208, 1999.  MR 1681815 |  Zbl 0937.53013
[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.  MR 2284293 |  Zbl 1121.13010
[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.  MR 2352606 |  Zbl 1145.53006
[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.  MR 3085676
[Hub09] E. Hubert. Differential invariants of a Lie group action: syzygies on a generating set. Journal of Symbolic Computation, 44(3):382–416, 2009.  MR 2494981 |  Zbl 1176.12004
[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.  MR 2365439 |  Zbl 1220.13003
[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.  MR 1846513 |  Zbl 0959.14029
[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.  MR 1309681 |  Zbl 0789.14008
[Ros56] M. Rosenlicht. Some basic theorems on algebraic groups. American Journal of Mathematics, 78:401–443, 1956.  MR 82183 |  Zbl 0073.37601
[Stu93] B. Sturmfels. Algorithms in invariant theory. Texts and Monographs in Symbolic Computation. Springer-Verlag, Vienna, 1993.  MR 1255980 |  Zbl 0802.13002
Copyright Cellule MathDoc 2017 | Crédit | Plan du site