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K-loops and Bruck loops on ℝ×ℝ

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Abstract

Using the function λ(x)=cosh x, K-loops on ℝ×ℝ are constructed. Since every K-loop is a Bruck loop, we have also examples for Bruck loops. Furthermore we investigate the group of the automorphisms δa,b of the K-loop which satisfy the equation a⊕(b⊕c)=(a⊕b)⊕δa,b(c).

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Authors and Affiliations

  1. Mathematisches Institut, Technische Universität München, Arcisstr. 21, 8000, München 2

    Alexander Kreuzer

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  1. Alexander Kreuzer
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Dedicated to Professor Dr. Oswald Giering on the occasion of his 60 th birthday

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Kreuzer, A. K-loops and Bruck loops on ℝ×ℝ. J Geom 47, 86–93 (1993). https://doi.org/10.1007/BF01223807

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  • DOI: https://doi.org/10.1007/BF01223807

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