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On automorphism groups of connected Lie groups

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Abstract

We prove that ifG is a connected Lie group with no compact central subgroup of positive dimension then the automorphism group ofG is an almost algebraic subgroup of\(GL(\mathcal{G})\), where\(\mathcal{G}\) is the Lie algebra ofG. We also give another proof of a theorem of D. Wigner, on the connected component of the identity in the automorphism group of a general connected Lie group being almost algebraic, and strengthen a result of M.Goto on the subgroup consisting of all automorphisms fixing a given central element.

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Authors and Affiliations

  1. Sonderforschungsbereich-170, Mathematisches Institut, Bunsenstrasse 3-5, D-34000, Göttingen, Germany

    S. G. Dani

  2. Mathematical Sciences Research Institute, 1000 Centennial Drive, 94720, Berkeley, CA, U.S.A.

    S. G. Dani

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  1. S. G. Dani
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Dani, S.G. On automorphism groups of connected Lie groups. Manuscripta Math 74, 445–452 (1992). https://doi.org/10.1007/BF02567680

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  • DOI: https://doi.org/10.1007/BF02567680

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