672
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Holomorphic Lie group actions on Danielewski surfaces

&
Pages 1801-1811 | Received 31 Jan 2022, Accepted 09 May 2022, Published online: 13 Jul 2022

References

  • Makar-Limanov L. On groups of automorphisms of a class of surfaces. Israel J Math. 1990;69(2):250–256.
  • Makar-Limanov L. On the group of automorphisms of a surface xny=P(z). Israel J Math. 2001;121:113–123.
  • Crachiola AJ. On automorphisms of Danielewski surfaces. J Algebraic Geom. 2006;15(1):111–132.
  • Daigle D. Locally nilpotent derivations and Danielewski surfaces. Osaka J Math. 2004;41(1):37–80.
  • Daigle D. On locally nilpotent derivations of kX1,X2,Y/(ϕ(Y)−X1X2). J Pure Appl Algebra. 2003;181(2–3):181–208.
  • Dubouloz A. Additive group actions on Danielewski varieties and the cancellation problem. Math Z. 2007;255(1):77–93.
  • Dubouloz A, Poloni PM. On a class of Danielewski surfaces in affine 3-space. J Algebra. 2009;321(7):1797–1812.
  • Kaliman S, Kutzschebauch F. Density property for hypersurfaces UV=P(X¯). Math Z. 2008;258(1):115–131.
  • Forstneri cˇ F, Kutzschebauch F. The first thirty years of Andersen–Lempert theory. arXiv:2111.08802.
  • Leuenberger M. Complete algebraic vector fields on Danielewski surfaces. Ann Inst Fourier (Grenoble). 2016;66(2):433–454.
  • Kutzschebauch F, Lind A. Holomorphic automorphisms of Danielewski surfaces I – density of the group of overshears. Proc Am Math Soc. 2011;139(11):3915–3927.
  • Andersén E, Lempert L. On the group of holomorphic automorphisms of Cn. Invent Math. 1992;110(2):371–388.
  • Andrist R, Kutzschebauch F, Lind A. Holomorphic automorphisms of Danielewski surfaces II – structure of the overshear group. Journal of Geometric Analysis, 25(3):1859–1889.
  • Ahern P, Rudin W. Periodic automorphisms of Cn. Indiana Univ Math J. 1995;44(1):287–303.
  • Kutzschebauch F, Kraft HP. Equivariant affine line bundles and linearization. Math Res Lett. 1996;3(5):619–627.
  • Andersén E. Algebraic and analytic properties of groups of holomorphic automorphisms of Cn [doctorial thesis]. Lund: Lunds tekniska högskola; 1994. ISSN:0347-8475.
  • De Fabritiis C. One-parameter groups of volume-preserving automorphisms of C2. Rend Istit Mat Univ Trieste. 1994;26(1–2):21–47.
  • Ahern P, Forstnerič F. One parameter automorphism groups on C2. Complex Var Theory Appl. 1995;27(3):245–268.
  • Ahern P, Forstnerič F, Varolin D. Flows on C2 with polynomial time one map. Complex Var Theory Appl. 1996;29(4):363–366.
  • Serre JP. Trees. Berlin: Springer-Verlag; 1980.
  • Silva Leite F. Bounds on the order of generation of SO(n,R) by one-parameter subgroups, current directions in nonlinear partial differential equations (Provo, UT, 1987). Rocky Mountain J Math. 1991;21(2):879–911.
  • Levi EE. Sulla struttura dei gruppi finiti e continui. In: Atti della Reale Accademia delle Scienze di Torino. B XL. 1905;551–565.
  • Iwasawa K. On some types of topological groups. Ann Math. 1949;50(3):507–558.
  • Malcev AI. On a class of homogeneous spaces. Izv Akad Nauk SSSR Ser Mat. 1949;13:9–32 [Russian].
  • Dynkin EB. Calculation of the coefficients in the Campbell–Hausdorff formula. Dokl Akad Nauk SSSR (NS). 1947;57:323–326 [Russian].
  • Akhiezer DN. Lie group actions in complex analysis. Braunschweig: Friedr. Vieweg Sohn; 1995. (Aspects of mathematics; E27).
  • Kutzschebauch F. Compact and reductive subgroups of the group of holomorphic automorphisms of Cn, singularities and complex analytic geometry (Japanese) (Kyoto, 1997). Surikaisekikenkyusho Kokyuroku. 1998;1033:81–93.
  • Andersén E. Volume-preserving automorphisms of Cn. Complex Var Theory Appl. 1990;14(1–4):223–235.
  • Kaliman S, Kutzschebauch F, Leuenberger M. Complete algebraic vector fields on affine surfaces. Int J Math. 2020;31(3):Article ID 2050018, 50 pp.