Advertisement

Reductive group actions with one-dimensional quotient

  • Hanspeter Kraft
  • Gerald W. Schwarz
Article

Keywords

Exact Sequence Vector Bundle Algebraic Group Group Scheme Linear Algebraic Group 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [BH1]
    H. Bass, W. Haboush, Linearizing certain reductive group actions,Trans. Amer. Math. Soc. 292 (1985), 463–482.zbMATHCrossRefGoogle Scholar
  2. [BH2]
    H. Bass, W. Haboush, Some equivariant K-theory of affine algebraic group actions,Comm. Algebra 15 (1987), 181–217.zbMATHCrossRefGoogle Scholar
  3. [Br]
    G. Bredon,Introduction to Compact Transformation Groups, Pure and Applied Mathematics vol.46, Academic Press, New York, 1972.Google Scholar
  4. [DG]
    M. Demazure, P. Gabriel,Groupes Algébriques, Masson, Paris-Amsterdam, 1970.zbMATHGoogle Scholar
  5. [Go]
    R. Godement,Topologie Algébrique et Théorie des Faisceaux, Publ. de l’Institut de Math. de l’Université de Strasbourg XIII, Hermann, Paris, 1964.Google Scholar
  6. [Gr]
    A. Grothendieck, Torsion homologique et sections rationnelles, inSéminaire Chevalley 1958, exposé no 5.Google Scholar
  7. [Ha]
    R. Hartshorne,Algebraic Geometry, Graduate Texts in Math. vol. 52, Springer Verlag, New York-Heidelberg-Berlin, 1977.zbMATHGoogle Scholar
  8. [Ka]
    T. Kambayashi, Automorphism group of a polynomial ring and algebraic group actions on an affine space,J. Algebra 60 (1979), 439–451.zbMATHCrossRefGoogle Scholar
  9. [Kn]
    F. Knop, Nichtlinearisierbare Operationen halbeinfacher Gruppen auf affinen Räumen,Invent. Math. 105 (1991), 217–220.zbMATHCrossRefGoogle Scholar
  10. [KoR1]
    M. Koras, P. Russell, On linearizing “good” C*-actions on C3, inGroup Actions and Invariant Theory, Can. Math. Soc. Conf. Proc. vol.10, 1989, pp. 93–102.Google Scholar
  11. [KoR2]
    M. Koras, P. Russell, Codimension 2 torus actions on affinen-space, inGroup Actions and Invariant Theory, Can. Math. Soc. Conf. Proc. vol.10, 1989, pp. 103–110.Google Scholar
  12. [Kr]
    H. Kraft,Geometrische Methoden in der Invariantentheorie, Aspekte der Mathematik vol.D1, Vieweg Verlag, Braunschweig, 1984.zbMATHGoogle Scholar
  13. [Kr1]
    H. Kraft, Algebraic automorphisms of affine space, inTopological Methods in Algebraic Transformation Groups, (eds. H. Kraft, T. Petrie, G. W. Schwarz), Progress in Mathematics vol.80, Birkhäuser Verlag, Basel-Boston, 1989, pp. 81–105.Google Scholar
  14. [Kr2]
    H. Kraft, G-vector bundles and the linearization problem, inGroup Actions and Invariant Theory, Can. Math. Soc. Conf. Proc. vol.10, 1989, pp. 111–123.Google Scholar
  15. [Kr3]
    H. Kraft, C*-actions on affine space, inOperator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory, Actes du colloque en l’honneur de Jacques Dixmier (eds. A. Connes, M. Duflo, A. Joseph, R. Rentschler), Progress in Mathematics vol.92, Birkhäuser Verlag, Basel-Boston, 1990, pp. 561–579.Google Scholar
  16. [KPR]
    H. Kraft, T. Petrie, J. Randall, Quotient varieties,Adv. Math. 74 (1989), 145–162.zbMATHCrossRefGoogle Scholar
  17. [KP]
    H. Kraft, V. L. Popov, Semisimple group actions on the three dimensional affine space are linear,Comment. Math. Helv. 60 (1985), 446–479.CrossRefGoogle Scholar
  18. [KS]
    H. Kraft andG. W. Schwarz, Reductive group actions on affine space with one-dimensional quotient, inGroup Actions and Invariant Theory, Can. Math. Soc. Conf. Proc. vol.10, 1989, pp. 125–132.Google Scholar
  19. [Li]
    P. Littelmann,On spherical double cones, to appear in J. Alg.Google Scholar
  20. [Lu]
    D. Luna, Slices étales,Bull. Soc. Math. France, Mémoire 33 (1973), 81–105.zbMATHGoogle Scholar
  21. [LR]
    D. Luna andR. W. Richardson, A generalization of the Chevalley restriction theorem,Duke Math. J. 46 (1979), 487–496.zbMATHCrossRefGoogle Scholar
  22. [MP]
    M. Masuda, T. Petrie, Equivariant algebraic vector bundles over representations of reductive groups: Theory,Proc. Nat. Acad. Sci. 88 (1991), 9061–9064.zbMATHCrossRefGoogle Scholar
  23. [MMP]
    M. Masuda, L. Moser-Jauslin, T. Petrie, Equivariant algebraic vector bundles over representations of reductive groups: Applications,Proc. Nat. Acad. Sci. 88 (1991), 9065–9066.zbMATHCrossRefGoogle Scholar
  24. [Pa]
    D. I. Panyushev, Semisimple automorphism groups of four-dimensional affine space,Math. USSR Izv. 23 (1984), 171–183.zbMATHCrossRefGoogle Scholar
  25. [Sch1]
    G. W. Schwarz, Representations of simple Lie groups with regular rings of invariants,Invent. Math. 49 (1978), 176–191.CrossRefGoogle Scholar
  26. [Sch2]
    G. W. Schwarz, Representations of simple Lie groups with a free module of covariants,Invent. Math. 50 (1978), 1–12.zbMATHCrossRefGoogle Scholar
  27. [Sch3]
    G. W. Schwarz, Lifting smooth homotopies of orbit spaces,Publ. Math. IHES 51 (1980), 37–135.zbMATHGoogle Scholar
  28. [Sch4]
    G. W. Schwarz, The topology of algebraic quotients, inTopological Methods in Algebraic Transformation Groups, (eds. H. Kraft, T. Petrie, G. W. Schwarz), Progress in Mathematics vol.10, Birkhäuser Verlag, Basel-Boston, 1989, pp. 135–152.Google Scholar
  29. [Sch5]
    G. W. Schwarz, Exotic algebraic group actions,C.R. Acad. Sci. Paris 309 (1989), 89–94.zbMATHGoogle Scholar
  30. [Se1]
    J.-P. Serre,Cohomologie Galoisienne, Lecture Notes in Mathematics vol.5, Springer Verlag, Berlin-Heidelberg-New York, 1965.zbMATHGoogle Scholar
  31. [Se2]
    J.-P. Serre,Corps Locaux, Publ. de l’Institut de Math. de l’Université de Nancago VIII, Hermann, Paris, 1968.Google Scholar
  32. [Se3]
    J.-P. serre, Espaces fibrés algébriques, inSéminaire Chevalley 1958, exposé no 5.Google Scholar
  33. [S1]
    P. Slodowy, Der Scheibensatz für algebraische Transformationsgruppen, inAlgebraic Transformation Groups and Invariant Theory, DMV Seminar vol.13, Birkhäuser Verlag, Basel-Boston, 1989, pp. 89–113.Google Scholar
  34. [St1]
    R. Steinberg, Regular elements of semisimple algebraic groups,Publ. Math. IHES,25 (1965), 49–80.Google Scholar
  35. [St2]
    R. Steinberg,Endomorphisms of linear algebraic groups, Mem. Amer. Math. Soc.80 (1968).Google Scholar

Copyright information

© Publications Mathématiques de L’I.H.É.S. 1992

Authors and Affiliations

  • Hanspeter Kraft
    • 1
    • 2
  • Gerald W. Schwarz
    • 1
    • 2
  1. 1.Mathematisches InstitutUniversität BaselBaselSwitzerland
  2. 2.Department of MathematicsBrandeis UniversityWalthamUSA

Personalised recommendations