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

Jan M. Myszewski — 1991

Annales Polonici Mathematici

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.

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

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