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The torsion form can be defined as the exterior covariant derivative of a solder form, $\Theta=d_\omega\theta$. This derivative is always in the fundamental representation of the algebra $\mathfrak g$ or it can be in any representation?

Namely $d_\omega\circ=(d + \omega\wedge_\rho)\circ$ with $\rho$ the fundamental representation of the algebra.

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    $\begingroup$ Would Mathematics be a better home for this question? $\endgroup$
    – Qmechanic ♦
    Commented Jul 4, 2019 at 10:01
  • $\begingroup$ Tried two times and nobody answered... $\endgroup$
    – Bellem
    Commented Jul 4, 2019 at 10:04
  • $\begingroup$ You should give a bit more detail here: is your solder form coming from a Cartan connection? What do you mean by "the fundamental representation"? For an arbitrary Lie algebra there is no fixed fundamental representation. $\endgroup$
    – ಠ_ಠ
    Commented Nov 30, 2021 at 8:04

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