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Tagged with differential-forms lie-algebras
3 questions
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Behaviour of the Cartan Maurer form
Let there be a Lie-group $G$ and its Lie-algebra $g$. Then the Cartan Maurer form is an 1-form $\omega: T_gG \rightarrow T_eG$ for which holds:
$$ (L^\ast_g)\omega = \omega$$
In Shlomo Sternberg's ...
- 700
8
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Simple identity on Lie algebras in a note of Koszul
In a 1947 Comptes Rendus note (T224, p. 448), Koszul makes the following claim (paraphrased, hopefully correctly), which seems like it should have a simple proof I am missing.
Given a compact, ...
- 2,995
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Exterior derivative on principal bundle [closed]
In Nakahara's Geometry, Topology and Physics on page 375, he constructs a Lie-algebra-valued one-form $\omega$ on a principal bundle $P$ by "lifting" a Lie-algebra-valued one-form $\mathcal A_i$ on an ...
- 541