Holomorphic automorphisms of some tube domains over non-selfadjoint cones

  • Laura Geatti


In this paper we determine the groups of all holomorphic automorphisms of a class of homogeneous non-symmetric domains. They are tube domains over some homogeneous non-selfadjoint cones, which are the natural generalization of the Vinberg cone and of its dual cone.


Semidirect Product Matrix Algebra Transitive Group Dual Cone Cone Versus 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Hirzebruch U.Halbraume und ihre holomorphen Automorphismen, Math. Ann.153 (1964), 395–417.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    Kaup W.,Einige Bemerkungen über polynomiale Vectorfelder, Jordan algebren und Automorphismen von Siegelschen Gebieten, Math. Ann.,204 (1973), 131–144.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Klingen H.,Analytic automorphisms of bounded symmetric complex domains, Pacific J. Math.10 (1960), 1327–1332.MATHMathSciNetGoogle Scholar
  4. [4]
    Kobayashi S.,Geometry of bounded domains, Trans. Am. Math. Soc.92 (1959), 267–290.MATHCrossRefGoogle Scholar
  5. [5]
    Geatti L.,Holomorphic Automorphisms of bounded homogeneous non-symmetric domains, Rend. Sem. Mat. Torino, (41)3 (1983), 203–218.MathSciNetGoogle Scholar
  6. [6]
    Geatti L.,Holomorphic automorphisms of the tube domain over the Vinberg cone, to appear on Atti Accad Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. S. VIII, vol. LXXX, (1986), 283–291.MathSciNetGoogle Scholar
  7. [7]
    Narasimhan R.,Several complex variables, Chicago Univ. Press (1971).Google Scholar
  8. [8]
    O'Connor M.A.,Cones, related T-algebras and affine geometries, Ph.d. dissertation, Univ. of Maryland (1980).Google Scholar
  9. [9]
    Siegel C.L.,Symplectic geometry, Amer. J. Math.65 (1943), 1–86.CrossRefMathSciNetGoogle Scholar
  10. [10]
    Vinberg E.B.,Homogeneous cones, Dokl. Akad. Nauk. SSSR133 (1960) 9–12= Soviet Math. Dokla.1 (1960), 787–790.MathSciNetGoogle Scholar
  11. [11]
    Vinberg E.B.,The theory of convex homogeneous cones, Trudy Moscow Math. Obsc.12 (1963), 303–353, Transl. Moscow Math. Soc.12 (1963), 340–403.MathSciNetGoogle Scholar

Copyright information

© Springer 1987

Authors and Affiliations

  • Laura Geatti
    • 1
  1. 1.Istituto di Elaborazione dell'Informazione del C.N.R.Pisa

Personalised recommendations