Lie algebra valued form

In differential geometry, a Lie algebra-valued form is a differential form with values in a Lie algebra. Such forms have important applications in the theory of connections on a principal bundle as well as in the theory of Cartan connections.

A Lie algebra-valued differential k-form on a manifold, ${\displaystyle M}$, is a smooth section of the bundle ${\displaystyle ({\mathfrak {g}}\times M)\otimes \Lambda ^{k}T^{*}M}$, where ${\displaystyle {\mathfrak {g}}}$ is a Lie algebra, ${\displaystyle T^{*}M}$ is the cotangent bundle of ${\displaystyle M}$ and Λ^k denotes the k^thexterior power.

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