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Hurwitz Pairs and Octonions

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Deformations of Mathematical Structures

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Abstract

It has been exhibited that all Hurwitz pairs (Vn,Sp) in case of p ≦ n ≦ 8 are only those for (n,p) = (1,1), (2,2), (4,3), (4,4), (8,5), (8,6), (8,7), and (8,8) ([1], [2]). A new matrix-multiplication law on M2(ℍ) compatible with the non-associative algebra O of octonions is introduced here. Our method makes the verification of the Hurwitz pair (ℝ8, ℝ8) easier and gives us a systematic view in the study of the pairs in case of p ≦ n ≦ 8.

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References

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Authors and Affiliations

  1. Department of Mathematics, Science University of Tokyo, Shinjuku-ku, Tokyo, Japan

    Shôji Kanemaki

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  1. Shôji Kanemaki
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Editors and Affiliations

  1. Institute of Mathematics of the Polish Academy of Sciences, Łódź, Poland

    Julian Ławrynowicz

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© 1989 Kluwer Academic Publishers

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Kanemaki, S. (1989). Hurwitz Pairs and Octonions. In: Ławrynowicz, J. (eds) Deformations of Mathematical Structures. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2643-1_20

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  • DOI: https://doi.org/10.1007/978-94-009-2643-1_20

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7693-7

  • Online ISBN: 978-94-009-2643-1

  • eBook Packages: Springer Book Archive

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