Rational Invariants of a Group Action

Evelyne Hubert[1]

  • [1] INRIA Méditerranée, France

Les cours du CIRM (2013)

  • Volume: 3, Issue: 1, page 1-10
  • ISSN: 2108-7164

Abstract

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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

How to cite

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Hubert, Evelyne. "Rational Invariants of a Group Action." Les cours du CIRM 3.1 (2013): 1-10. <http://eudml.org/doc/275491>.

@article{Hubert2013,
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},
affiliation = {INRIA Méditerranée, France},
author = {Hubert, Evelyne},
journal = {Les cours du CIRM},
language = {eng},
number = {1},
pages = {1-10},
publisher = {CIRM},
title = {Rational Invariants of a Group Action},
url = {http://eudml.org/doc/275491},
volume = {3},
year = {2013},
}

TY - JOUR
AU - Hubert, Evelyne
TI - Rational Invariants of a Group Action
JO - Les cours du CIRM
PY - 2013
PB - CIRM
VL - 3
IS - 1
SP - 1
EP - 10
AB - 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
LA - eng
UR - http://eudml.org/doc/275491
ER -

References

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  2. H. Derksen and G. Kemper. Computational invariant theory. Invariant Theory and Algebraic Transformation Groups I. Springer-Verlag, Berlin, 2002. Encyclopaedia of Math. Sc., 130. Zbl1011.13003MR1918599
  3. M. Fels and P. J. Olver. Moving coframes. II. Regularization and theoretical foundations. Acta Appl. Math., 55(2):127–208, 1999. Zbl0937.53013MR1681815
  4. 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. Zbl1121.13010MR2284293
  5. 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. Zbl1145.53006MR2352606
  6. 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. Zbl1323.68605
  7. E. Hubert and G. Labahn. Scaling invariants and symmetry reduction of dynamical systems. Foundations of Computational Mathematics, 2013. Zbl1284.34045MR3085676
  8. E. Hubert. Differential invariants of a Lie group action: syzygies on a generating set. Journal of Symbolic Computation, 44(3):382–416, 2009. Zbl1176.12004MR2494981
  9. 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. 
  10. G. Kemper. The computation of invariant fields and a new proof of a theorem by Rosenlicht. Transformation Groups, 12:657–670, 2007. Zbl1220.13003MR2365439
  11. 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. Zbl0959.14029MR1846513
  12. 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. Zbl0789.14008MR1309681
  13. M. Rosenlicht. Some basic theorems on algebraic groups. American Journal of Mathematics, 78:401–443, 1956. Zbl0073.37601MR82183
  14. B. Sturmfels. Algorithms in invariant theory. Texts and Monographs in Symbolic Computation. Springer-Verlag, Vienna, 1993. Zbl0802.13002MR1255980

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