Enviar artigo por via de e-mail The Lengths of the Quaternion and Octonion Algebras
- Autores: Guterman A.E.1,2, Kudryavtsev D.K.1
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Afiliações:
- Lomonosov Moscow State University
- Moscow Center for Continuous Mathematical Education
- Edição: Volume 224, Nº 6 (2017)
- Páginas: 826-832
- Seção: 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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Resumo
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.
Sobre autores
A. Guterman
Lomonosov Moscow State University; Moscow Center for Continuous Mathematical Education
Autor responsável pela correspondência
Email: alexander.guterman@gmail.com
Rússia, Moscow
D. Kudryavtsev
Lomonosov Moscow State University
Email: alexander.guterman@gmail.com
Rússia, Moscow
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