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Mathematics > Group Theory
Title: On the commutator length of compact Lie groups
(Submitted on 5 Sep 2023)
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.
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