nLab adjoint bundle

Definition

For $G$ a Lie group and $\mathfrak{g}$ its Lie algebra, and for $P \to X$ a $G$-principal bundle, the corresponding adjoint bundle is the associated bundle $P \times_G \mathfrak{g} \to X$ via the adjoint action/adjoint representation of $G$ on $\mathfrak{g}$.

Related concepts

• Atiyah Lie algebroid