The Lengths of the Quaternion and Octonion Algebras
| Autor: | D. K. Kudryavtsev, Alexander Guterman |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Discrete mathematics Applied Mathematics General Mathematics 010102 general mathematics Zero (complex analysis) 010103 numerical & computational mathematics Division (mathematics) 01 natural sciences Octonion 0101 mathematics Algebra over a field Quaternion Complex number Real number Mathematics |
| Zdroj: | Journal of Mathematical Sciences. 224:826-832 |
| ISSN: | 1573-8795 1072-3374 |
| DOI: | 10.1007/s10958-017-3453-x |
| Popis: | 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 (𝕆). 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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