English

On the commutator length of compact Lie groups

Group Theory 2023-09-06 v1 Algebraic Topology

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.

Keywords

Cite

@article{arxiv.2309.02344,
  title  = {On the commutator length of compact Lie groups},
  author = {Juan Omar Gómez and Victor Torres-Castillo and Bernardo Villarreal},
  journal= {arXiv preprint arXiv:2309.02344},
  year   = {2023}
}

Comments

6 pages, comments welcome!