On automorphism groups of connected lie groups

Dani, S. G. (1992) On automorphism groups of connected lie groups Manuscripta Mathematica, 74 (1). pp. 445-452. ISSN 0025-2611

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Official URL: http://www.springerlink.com/content/31523556075206...

Related URL: http://dx.doi.org/10.1007/BF02567680


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(G), where 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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