Email this article The Lengths of the Quaternion and Octonion Algebras
- Authors: Guterman A.E.1,2, Kudryavtsev D.K.1
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Affiliations:
- Lomonosov Moscow State University
- Moscow Center for Continuous Mathematical Education
- Issue: Vol 224, No 6 (2017)
- Pages: 826-832
- Section: Article
- URL: https://ogarev-online.ru/1072-3374/article/view/239695
- DOI: https://doi.org/10.1007/s10958-017-3453-x
- ID: 239695
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Abstract
The classical Hurwitz theorem claims that there are exactly four normed algebras with division: the real numbers (ℝ), complex numbers (ℂ), quaternions (ℍ), and octonions (????). The length of ℝ as an algebra over itself is zero; the length of ℂ as an ℝ-algebra equals one. The purpose of the present paper is to prove that the lengths of the ℝ-algebras of quaternions and octonions equal two and three, respectively.
About the authors
A. E. Guterman
Lomonosov Moscow State University; Moscow Center for Continuous Mathematical Education
Author for correspondence.
Email: alexander.guterman@gmail.com
Russian Federation, Moscow
D. K. Kudryavtsev
Lomonosov Moscow State University
Email: alexander.guterman@gmail.com
Russian Federation, Moscow
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