Loops as sections in compact Lie groups
Representation Theory
2015-02-25 v1 Group Theory
Geometric Topology
Abstract
We prove that there does not exist any connected topological proper loop homeomorphic to a quasi-simple Lie group and having a compact Lie group as the group topologically generated by its left translations. Moreover, any connected topological loop homeomorphic to the 7-sphere and having a compact Lie group as the group of its left translations is classical. We give a particular simple general construction for proper loops such that the compact group of their left translations is direct product of at least 3 factors.
Keywords
Cite
@article{arxiv.1502.06911,
title = {Loops as sections in compact Lie groups},
author = {Agota Figula and Karl Strambach},
journal= {arXiv preprint arXiv:1502.06911},
year = {2015}
}