Skip to main content

The algebra of invariants

  • 1083 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 585)

Keywords

  • Algebraic Group
  • Invariant Theory
  • Finite Type
  • Rational Representation
  • Homogeneous Element

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   39.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References for Ch.2.

  1. A. Borel, Linear algebraic groups, New York, W.A.Benjamin, 1969.

    MATH  Google Scholar 

  2. N. Bourbaki, Groupes et algèbres de Lie, Chap.4,5,6, Paris, Hermann, 1968.

    Google Scholar 

  3. H.Cartan and S.Eilenberg, Homological algebra, Princeton Univ.Press 1956.

    Google Scholar 

  4. A.Cayley, A second memoir upon quantics, Coll.Math.Papers II, 250–275, Cambridge University Press, 1889.

    Google Scholar 

  5. M.Demazure, Démonstration de la conjecture de Mumford (d'après W.Haboush), Sém. Bourbaki no.462, 1974/75.

    Google Scholar 

  6. J. Dieudonné and J.B. Carrell, Invariant theory, old and new, New York, Acad.Press, 1971.

    MATH  Google Scholar 

  7. P. Gordan, Beweis, dass jede Covariante und Invariante einer binären Form eine ganze Function mit numerischen Coefficienten einer endlichen Anzahl solcher Formen ist, J.f.d.reine u.angew.Math., 69 (1868), 323–354.

    CrossRef  MathSciNet  Google Scholar 

  8. W.J. Haboush, Reductive groups are geometrically reductive, Ann. of Math. 102 (1975), 67–83.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. D.Hilbert, Über die Theorie der algebraischen Formen, Ges.Abh., II2, 199–257, Springer-Verlag, 1970.

    Google Scholar 

  10. D.Hilbert, Über die vollen Invariantensysteme, Ges.Abh., II2, 287–344, Springer-Verlag, 1970.

    Google Scholar 

  11. D.Hilbert, Mathematische Probleme, Ges.Abh., III2, 290–329, Springer-Verlag, 1970.

    Google Scholar 

  12. A. Hurwitz, Über die Erzeugung der Invarianten durch Integration, Ges.Werke II, 546–564, Basel, Birkhäuser, 1933.

    Google Scholar 

  13. S.Lang, Algebra, Addison-Wesley, 1965.

    Google Scholar 

  14. D.Mumford, Geometric invariant theory, Erg.d.Math. Bd.34, Springer-Verlag, 1965.

    Google Scholar 

  15. M. Nagata, On the 14th problem of Hilbert, Am.J.Math.81 (1959), 766–772.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. M. Nagata, Complete reducibility of rational representations of a matric group, J.Math.Kyoto Univ. 1 (1961), 87–99.

    MathSciNet  MATH  Google Scholar 

  17. M. Nagata, Invariants of a group in an affine ring, J.Math.Kyoto Univ. 3 (1964), 369–377.

    MathSciNet  MATH  Google Scholar 

  18. M Nagata and T. Miyota, Note on semi-reductive groups, J.Math.Kyoto Univ. 3 (1964), 379–382.

    MathSciNet  MATH  Google Scholar 

  19. E. Noether, Körper und Systeme rationaler Funktionen, Math.Ann. 76 (1915), 161–196.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. E.Noether, Der Endlichkeitssatz der Invariantentheorie endlicher linearer Gruppen der Charakteristik p, Nachr. Ges.d.Wiss. Göttingen (1926), 28–35.

    Google Scholar 

  21. M. Rosenlicht, A remark on quotient spaces, An.Ac.Bras.Cienc. 35 (1963), 487–489.

    MathSciNet  MATH  Google Scholar 

  22. C.S. Seshadri, On a theorem of Weitzenböck in invariant theory, J.Math.Kyoto Univ. 1 (1961), 403–409.

    MathSciNet  MATH  Google Scholar 

  23. H.Weyl, Theorie der Darstellung kontinuierlicher halbeinfacher Gruppen durch lineare Transformationen, Ges.Abh.II, 543–647, Springer-Verlag, 1968.

    Google Scholar 

Download references

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 1977 Springer-Verlag

About this chapter

Cite this chapter

Springer, T.A. (1977). The algebra of invariants. In: Invariant Theory. Lecture Notes in Mathematics, vol 585. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0095646

Download citation

  • DOI: https://doi.org/10.1007/BFb0095646

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08242-2

  • Online ISBN: 978-3-540-37370-4

  • eBook Packages: Springer Book Archive