On systems of orthogonal permutations |
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| Author |
Department of Mechanics and Mathematics, Kyiv Taras Shevcnenko University
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| Abstract |
We introduce the notion of complete system of orthogonal permutations in
$\Bbb R^n$ and show that any such system generates a structure of divisions
algebra in $\Bbb R^n$. We describe the systems of orthogonal permutations
that correspond to the~fields of real and complex numbers, the skew field of
quaternions and, the Cayley algebra.
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| Keywords |
orthogonal permutations, complete system, division algebra, complex numbers, Cayley algebra
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| DOI |
doi:10.30970/ms.12.1.3-6
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Reference |
1. Adams J.F. On the non-existence of elements of Hopf invariant one // Math. Ann. – 1960 V. 72 p. 20–104
2. Kurosh A.G. Lectures on General Algebra , Nauka ,addr Moscow – 1962 in Russian |
| Pages |
3-6
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| Volume |
12
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| Issue |
1
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| Year |
1999
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| Journal |
Matematychni Studii
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| Full text of paper | |
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