Loops as sections in compact Lie groups

2015/02/21 by Agota Figula, Figula, Agota, Karl Strambach +1
Mathematics · #20N05 #22C05 #57T15 #57T20 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.GT #math.RT #msc:20N05 #msc:22C05 #msc:57T15 #msc:57T20

paper · pdf · doi:10.48550/arxiv.1502.06911

arxiv created 2015/02/21 · arxiv updated 2015/02/25

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.

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