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!