Hurwitz Pairs and Octonions

Shôji Kanemaki
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Shôji Kanemaki: Science University of Tokyo, Department of Mathematics

A chapter in Deformations of Mathematical Structures, 1989, pp 215-223 from Springer

Abstract: 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.

Keywords: Division Algebra; Bilinear Mapping; Octonion Algebra; Vector Cross Product; Usual Euclidean Norm (search for similar items in EconPapers)
Date: 1989
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-2643-1_20

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DOI: 10.1007/978-94-009-2643-1_20

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