Timeline for Gauge connections and Lie algebras?
Current License: CC BY-SA 2.5
3 events
| when toggle format | what | by | license | comment | |
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| Mar 18, 2010 at 15:13 | history | edited | José Figueroa-O'Farrill | CC BY-SA 2.5 |
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| Mar 18, 2010 at 8:30 | comment | added | Sebastian | I think the connection form $\theta$ does not libe in the bundle of the adjoint representation of $G:$ To see this, note that the vertical bundle $V=\ker d\pi$ I canonically isomorphic to $M\times g.$ A (gerneralized connection is (as you said) an complementary bundle $H\subset TP$ of $V.$ Thus, any complementary bundle is the kernel of the corresponding projection onto $V,$ forgetting about the $M$ part gives you a well-defined 1-form $\theta$ on $P$ with values in $g.$ | |
| Jan 18, 2010 at 23:37 | history | answered | José Figueroa-O'Farrill | CC BY-SA 2.5 |