Reductive group actions with one-dimensional quotient
Publications Mathématiques de l'IHÉS, Volume 76 (1992), pp. 1-97.
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     author = {Kraft, Hanspeter and Schwarz, Gerald W.},
     title = {Reductive group actions with one-dimensional quotient},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {1--97},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {76},
     year = {1992},
     mrnumber = {1215592},
     zbl = {0783.14026},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_1992__76__1_0/}
}
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Kraft, Hanspeter; Schwarz, Gerald W. Reductive group actions with one-dimensional quotient. Publications Mathématiques de l'IHÉS, Volume 76 (1992), pp. 1-97. http://www.numdam.org/item/PMIHES_1992__76__1_0/

[BH1] H. Bass, W. Haboush, Linearizing certain reductive group actions, Trans. Amer. Math. Soc. 292 (1985), 463-482. | MR | Zbl

[BH2] H. Bass, W. Haboush, Some equivariant K-theory of affine algebraic group actions, Comm. Algebra 15 (1987), 181-217. | MR | Zbl

[Br] G. Bredon, Introduction to Compact Transformation Groups, Pure and Applied Mathematics vol. 46, Academic Press, New York, 1972. | MR | Zbl

[DG] M. Demazure, P. Gabriel, Groupes Algébriques, Masson, Paris-Amsterdam, 1970. | Zbl

[Go] R. Godement, Topologie Algébrique et Théorie des Faisceaux, Publ. de l'Institut de Math. de l'Université de Strasbourg XIII, Hermann, Paris, 1964. | Zbl

[Gr] A. Grothendieck, Torsion homologique et sections rationnelles, in Séminaire Chevalley 1958, exposé n° 5. | Numdam

[Ha] R. Hartshorne, Algebraic Geometry, Graduate Texts in Math. vol. 52, Springer Verlag, New York-Heidelberg-Berlin, 1977. | MR | Zbl

[Ka] T. Kambayashi, Automorphism group of a polynomial ring and algebraic group actions on an affine space, J. Algebra 60 (1979), 439-451. | MR | Zbl

[Kn] F. Knop, Nichtlinearisierbare Operationen halbeinfacher Gruppen auf affinen Räumen, Invent. Math. 105 (1991), 217-220. | MR | Zbl

[KoR1] M. Koras, P. Russell, On linearizing "good" C*-actions on C3, in Group Actions and Invariant Theory, Can. Math. Soc. Conf. Proc. vol. 10, 1989, pp.93-102. | MR | Zbl

[KoR2] M. Koras, P. Russell, Codimension 2 torus actions on affine n-space, in Group Actions and Invariant Theory, Can. Math. Soc. Conf. Proc. vol. 10, 1989, pp. 103-110. | MR | Zbl

[Kr] H. Kraft, Geometrische Methoden in der Invariantentheorie, Aspekte der Mathematik vol. D1, Vieweg Verlag, Braunschweig, 1984. | MR | Zbl

[Kr1] H. Kraft, Algebraic automorphisms of affine space, in Topological 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. | MR | Zbl

[Kr2] H. Kraft, G-vector bundles and the linearization problem, in Group Actions and Invariant Theory, Can. Math. Soc. Conf. Proc. vol. 10, 1989, pp. 111-123. | MR | Zbl

[Kr3] H. Kraft, C*-actions on affine space, in Operator 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. | MR | Zbl

[KPR] H. Kraft, T. Petrie, J. Randall, Quotient varieties, Adv. Math. 74 (1989), 145-162. | MR | Zbl

[KP] H. Kraft, V. L. Popov, Semisimple group actions on the three dimensional affine space are linear, Comment. Math. Helv. 60 (1985), 446-479. | Zbl

[KS] H. Kraft and G. W. Schwarz, Reductive group actions on affine space with one-dimensional quotient, in Group Actions and Invariant Theory, Can. Math. Soc. Conf. Proc. vol. 10, 1989, pp. 125-132. | Zbl

[Li] P. Littelmann, On spherical double cones, to appear in J. Alg. | Zbl

[Lu] D. Luna, Slices étales, Bull. Soc. Math. France, Mémoire 33 (1973), 81-105. | Numdam | MR | Zbl

[LR] D. Luna and R. W. Richardson, A generalization of the Chevalley restriction theorem, Duke Math. J. 46 (1979), 487-496. | MR | Zbl

[MP] M. Masuda, T. Petrie, Equivariant algebraic vector bundles over representations of reductive groups: Theory, Proc. Nat. Acad. Sci. 88 (1991), 9061-9064. | MR | Zbl

[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. | MR | Zbl

[Pa] D. I. Panyushev, Semisimple automorphism groups of four-dimensional affine space, Math. USSR Izv. 23 (1984), 171-183. | Zbl

[Sch1] G. W. Schwarz, Representations of simple Lie groups with regular rings of invariants, Invent. Math. 49 (1978), 176-191. | MR | Zbl

[Sch2] G. W. Schwarz, Representations of simple Lie groups with a free module of covariants, Invent. Math. 50 (1978), 1-12. | MR | Zbl

[Sch3] G. W. Schwarz, Lifting smooth homotopies of orbit spaces, Publ. Math. IHES 51 (1980), 37-135. | Numdam | MR | Zbl

[Sch4] G. W. Schwarz, The topology of algebraic quotients, in Topological 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. | MR | Zbl

[Sch5] G. W. Schwarz, Exotic algebraic group actions, C.R. Acad. Sci. Paris 309 (1989), 89-94. | MR | Zbl

[Se1] J.-P. Serre, Cohomologie Galoisienne, Lecture Notes in Mathematics vol. 5, Springer Verlag, Berlin-Heidelberg-New York, 1965. | MR | Zbl

[Se2] J.-P. Serre, Corps Locaux, Publ. de l'Institut de Math. de l'Université de Nancago VIII, Hermann, Paris, 1968. | MR

[Se3] J.-P. Serre, Espaces fibrés algébriques, in Séminaire Chevalley 1958, exposé n° 5. | Numdam

[Sl] P. Slodowy, Der Scheibensatz für algebraische Transformationsgruppen, in Algebraic Transformation Groups and Invariant Theory, DMV Seminar vol. 13, Birkhäuser Verlag, Basel-Boston, 1989, pp. 89-113. | MR | Zbl

[St1] R. Steinberg, Regular elements of semisimple algebraic groups, Publ. Math. IHES, 25 (1965), 49-80. | Numdam | MR | Zbl

[St2] R. Steinberg, Endomorphisms of linear algebraic groups, Mem. Amer. Math. Soc. 80 (1968). | MR | Zbl