Adjoint bundle
= Adjoint bundle
{title2=$\operatorname{ad}P=P\times_{\operatorname{Ad}}\mathfrak g$}
The adjoint bundle is the <associated vector bundle> for the <Adjoint representation of a Lie group> on its <Lie algebra>. The <gauge curvature> of a <principal connection> is globally a two-form with values in this bundle. Differences of <principal connections> and their infinitesimal variations are one-forms with values in the same bundle.