On the commutator length of compact Lie groups

2023/09/05 by Juan Omar Gómez, Gómez, Juan Omar, Victor Torres-Castillo +3
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2309.02344

openalex publication_date 2023/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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