On the commutator length of compact Lie groups (2309.02344v1)

Abstract: In this short note we show that the path-connected component of the identity of the derived subgroup of a compact Lie group consists just of commutators. We also discuss an application of our main result to the homotopy type of the classifying space for commutativity for a compact Lie group whose path-connected component of the identity is abelian.