On roots of the automorphism group of a circular domain in $ℂ^n$

• Autorzy: Jan M. Myszewski
• Języki publikacji: EN

Abstrakty

EN

We study the properties of the group Aut(D) of all biholomorphic transformations of a bounded circular domain D in $ℂ^n$ containing the origin. We characterize the set of all possible roots for the Lie algebra of Aut(D). There exists an n-element set P such that any root is of the form α or -α or α-β for suitable α,β ∈ P.

Słowa kluczowe

EN

circular domain; automorphism group; maximal torus; Lie algebra; adjoint representation; root; root subspace

Kategorie tematyczne

• 32A07: Special domains (Reinhardt, Hartogs, circular, tube)
• 17B05: Structure theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1991
• Tom: 55
• Numer: 1
• Strony: 269-276

Daty

wydano

1991

otrzymano

1990-09-14

poprawiono

1991-01-10

Twórcy

autor

Jan M. Myszewski

• Institute of Applications of Mathematics, SGGW-academy of Agriculture, Nowoursynowska 166, 02-975 Warszawa, Poland

Bibliografia

• [1] J. F. Adams, Lectures on Lie Groups, Benjamin, New York 1969.
• [2] W. Kaup and H. Upmeier, Banach spaces with biholomorphically equivalent balls are isomorphic, Proc. Amer. Math. Soc. 58 (1976), 129-133.
• [3] J. M. Myszewski, On maximal tori of the automorphism group of circular domain in $ℂ^n$, Demonstratio Math. 22 (4) (1989), 1067-1080.
• [4] R. Narasimhan, Several Complex Variables, Chicago Lectures in Mathematics, The University of Chicago Press, Chicago & London 1971.
• [5] T. Sunada, Holomorphic equivalence problem for bounded Reinhardt domains, Math. Ann. 235 (1978), 111-128.