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An important case of vector-valued differential forms are [[Lie algebra-valued forms]]. (A [[connection form]] is an example of such a form.)
==Definition==
Let ''M'' be a [[smooth manifold]] and ''E'' → ''M'' be a smooth [[vector bundle]] over ''M''. We denote the space of [[section (fiber bundle)|smooth section]]s of a bundle ''E'' by Γ(''E''). An '''''E''-valued differential form''' of degree ''p'' is a smooth section of the [[tensor product bundle]] of ''E'' with Λ<sup>''p''</sup>(''T''<sup> ∗</sup>''M''), the ''p''-th [[exterior power]] of the [[cotangent bundle]] of ''M''. The space of such forms is denoted by
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