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Loops as sections in compact Lie groups

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Abstract

We show 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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Authors and Affiliations

  1. Institute of Mathematics, University of Debrecen, P.O.Box 400, 4002, Debrecen, Hungary

    Á. Figula

  2. Department Mathematik, Universität Erlangen-Nürnberg, Cauerstrasse 11, 91058, Erlangen, Germany

    K. Strambach

Authors
  1. Á. Figula
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  2. K. Strambach
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Correspondence to Á. Figula.

Additional information

Communicated by Ulf Kühn and Ingo Runkel.

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Figula, Á., Strambach, K. Loops as sections in compact Lie groups. Abh. Math. Semin. Univ. Hambg. 87, 61–68 (2017). https://doi.org/10.1007/s12188-016-0128-3

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  • DOI: https://doi.org/10.1007/s12188-016-0128-3

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