Loops on spheres having a compact-free inner mapping group

摘要

We prove that any topological loop homeomorphic to a sphere or to a real projective space and having a compact-free Lie group as the inner mapping group is homeomorphic to the circle. Moreover, we classify the differentiable 1-dimensional compact loops explicitly using the theory of Fourier series. 2000 Mathematics Subject Classification: 22A30, 22E99, 20N05, 57S20, 22F30Key words: Locally compact loops, differentiable loops, multiplications on spheresAuthors’ addresses: Ágota Figula, Mathematisches Institut der Universität Erlangen-Nürnberg, Bismarckstr. 1 1/2, 91054 Erlangen, Germany and Institute of Mathematics, University of Debrecen, P.O.B. 12, H-4010 Debrecen, Hungary; Karl Strambach, Mathematisches Institut der Universität Erlangen-Nürnberg, Bismarckstr. 1 1/2, 91054 Erlangen, Germany