Advertisement

U-Projectors and Fields of U-Invariants

  • K. A. VyatkinaEmail author
  • A. N. Panov
Article

Abstract

We present a general construction of the U-projector (the homomorphism of an algebra into its field of U-invariants identical on the subalgebra of U-invariants). It is shown how to apply the U-projector to find the systems of free generators of the fields of U-invariants for representations of reductive groups.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. Dixmier, Algèbres enveloppantes, Gauthier-Villars, Paris (1974).zbMATHGoogle Scholar
  2. 2.
    A. Joseph, “A preparation theorem for the prime spectrum of a semisimple Lie algebra,” J. Algebra, 48, 241–289 (1977).MathSciNetCrossRefGoogle Scholar
  3. 3.
    K. Miyata, “Invariants of certain groups,” Nagoya Math. J., 41, 69–73 (1971).MathSciNetCrossRefGoogle Scholar
  4. 4.
    L. Pukanszky, Leçons sur les représentations des groupes, Monogr. Soc. Math. France, Dunod, Paris (1967).Google Scholar
  5. 5.
    E. B. Vinberg, “Rationality of the field of invariants of the triangular group,” Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 2, 23–24 (1982).Google Scholar
  6. 6.
    E. B. Vinberg and V. L. Popov, “Invariant theory,” in: Algebraic Geometry IV, Encycl. Math. Sci., Vol. 55, Springer, Berlin (1994), pp. 123–284.Google Scholar
  7. 7.
    K. A. Vyatkina and A. N. Panov, “Field of U-invariants of adjoint representation of the group GL(n,K),” Mat. Zametki, 93, 144–147 (2013).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Samara UniversitySamaraRussia

Personalised recommendations