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The holomorphic automorphism group of the complex disk

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Abstract

The group of all holomorphic automorphisms of the complex unit disk consists of Möbius transformations involving translation-like holomorphic automorphisms and rotations. The former are calledgyrotranslations. As opposed to translations of the complex Plane, which are associative-commutative operations forming a group, gyrotranslations of the complex unit disk fail to form a group. Rather, left gyrotranslations are gyroassociative-gyrocommutative operations forming agyrogroup.

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  1. Department of Mathematics, North Dakota State University, 58105, Fargo, ND, USA

    Abraham A. Ungar

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  1. Abraham A. Ungar
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Ungar, A.A. The holomorphic automorphism group of the complex disk. Aeq. Math. 47, 240–254 (1994). https://doi.org/10.1007/BF01832962

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