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

Jan Myszewski

ArticleOriginal scientific text

Title

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

Authors ¹

Affiliations

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

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.

Keywords

ENG

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

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R. Narasimhan, Several Complex Variables, Chicago Lectures in Mathematics, The University of Chicago Press, Chicago & London 1971.
T. Sunada, Holomorphic equivalence problem for bounded Reinhardt domains, Math. Ann. 235 (1978), 111-128.

Title

On roots of the automorphism group of a circular domain in ℂn

Affiliations

Abstract

Keywords

Bibliography

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