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

Jan M. Myszewski

Annales Polonici Mathematici (1991)

  • Volume: 55, Issue: 1, page 269-276
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Jan M. Myszewski. "On roots of the automorphism group of a circular domain in $ℂ^n$." Annales Polonici Mathematici 55.1 (1991): 269-276. <http://eudml.org/doc/262279>.

@article{JanM1991,
abstract = {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.},
author = {Jan M. Myszewski},
journal = {Annales Polonici Mathematici},
keywords = {circular domain; automorphism group; maximal torus; Lie algebra; adjoint representation; root; root subspace; bounded circular domain in ; Lie algebras of real vector fields},
language = {eng},
number = {1},
pages = {269-276},
title = {On roots of the automorphism group of a circular domain in $ℂ^n$},
url = {http://eudml.org/doc/262279},
volume = {55},
year = {1991},
}

TY - JOUR
AU - Jan M. Myszewski
TI - On roots of the automorphism group of a circular domain in $ℂ^n$
JO - Annales Polonici Mathematici
PY - 1991
VL - 55
IS - 1
SP - 269
EP - 276
AB - 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.
LA - eng
KW - circular domain; automorphism group; maximal torus; Lie algebra; adjoint representation; root; root subspace; bounded circular domain in ; Lie algebras of real vector fields
UR - http://eudml.org/doc/262279
ER -

References

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  1. [1] J. F. Adams, Lectures on Lie Groups, Benjamin, New York 1969. Zbl0206.31604
  2. [2] W. Kaup and H. Upmeier, Banach spaces with biholomorphically equivalent balls are isomorphic, Proc. Amer. Math. Soc. 58 (1976), 129-133. Zbl0337.32012
  3. [3] J. M. Myszewski, On maximal tori of the automorphism group of circular domain in ℂ n , Demonstratio Math. 22 (4) (1989), 1067-1080. Zbl0765.32001
  4. [4] R. Narasimhan, Several Complex Variables, Chicago Lectures in Mathematics, The University of Chicago Press, Chicago & London 1971. Zbl0223.32001
  5. [5] T. Sunada, Holomorphic equivalence problem for bounded Reinhardt domains, Math. Ann. 235 (1978), 111-128. Zbl0357.32001

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