Re: Lie Algebren

Robert Grap wrote:

Aber anscheinend war mein Schluss "Lie Gruppe = Gruppe als Mannigfaltigkeit
=> Lie Algebra = Algebra als Mannigfaltigkeit" etwas vorschnell, wie ich im
Link von Rainer lesen konnte...

Penrose beschreibt den "Unterschied" in Road to Reality so:

"
Fig. 13.12
The Lie algebra for a (faithful) representation of a
Lie group G (basically, knowledge of the structure constants
gamma_ab^x) determines the local structure of G, i.e. it
fixes the structure of G within some (sufficiently small)
open region N surrounding the identity element I, but it
does not tell us about the global nature of G."

(Das Bild zeigt eine Region N auf einem Torus G.)

Du kannst also etwa hier weiterschauen:
http://de.wikipedia.org/wiki/Darstellungstheorie
.

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