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Historical Remarks on the Surjectivity of the Exponential Function of Lie Groups

✍ Scribed by Michael Wüstner

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
82 KB
Volume
29
Category
Article
ISSN
0315-0860

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✦ Synopsis

In 1892, F. Engel and E. Study investigated the exponential map of classical Lie groups for the first time. They showed that the special projective Lie groups over C possess surjective exponential functions. Engel also gave a "proof" for the corresponding claims for the other projective classical groups. However, it is known that the latter claims are wrong. Nevertheless, these "results" are still cited in the literature without comments. In the present paper, the mentioned works of Engel and Study are critically discussed. C 2002 Elsevier Science (USA) Im Jahre 1892 untersuchten F. Engel und E. Study als erste die Exponentialfunktion klassischer Lie-Gruppen. Sie zeigten, daß die speziellen projektiven Lie-Gruppen über C eine surjektive Exponentialfunktion besitzen. Engel formulierte auch einen ,,Beweis" für die entsprechenden Aussagen über die anderen projektiven klassischen Gruppen. Inzwischen weiß man, daß die letzteren Aussagen jedoch falsch sind. Dennoch werden jene ,,Ergebnisse" immer noch unkommentiert in der Literatur zitiert. Im vorliegendein in Artikel werden die besagten Arbeiten von Engel und Study kritisch diskutiert.

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