A Mnemonic Matrix Rule for (Split) Octonionic Multiplication and its Extension to the Cayley--Dickson Tower
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911398758449152 |
|---|---|
| author | Gazeau, Jean-Pierre |
| author_facet | Gazeau, Jean-Pierre |
| contents | We present a compact mnemonic device for computing the product of two (split) octonions written in Cayley--Dickson form q+l p with q,p in H. The rule appears as a simple (R+L) pattern of right-ordered and left-ordered (quaternionic) products inside a 2X2 quaternionic matrix model. The pattern extends verbatim to all algebras in the Cayley--Dickson tower, providing an efficient computational tool in non-associative settings. To our knowledge, this explicit ``(R+L)'' mnemonic does not appear in the classical literature on octonions or composition algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22134 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Mnemonic Matrix Rule for (Split) Octonionic Multiplication and its Extension to the Cayley--Dickson Tower Gazeau, Jean-Pierre Rings and Algebras 81R12, 11R52, 17A01 We present a compact mnemonic device for computing the product of two (split) octonions written in Cayley--Dickson form q+l p with q,p in H. The rule appears as a simple (R+L) pattern of right-ordered and left-ordered (quaternionic) products inside a 2X2 quaternionic matrix model. The pattern extends verbatim to all algebras in the Cayley--Dickson tower, providing an efficient computational tool in non-associative settings. To our knowledge, this explicit ``(R+L)'' mnemonic does not appear in the classical literature on octonions or composition algebras. |
| title | A Mnemonic Matrix Rule for (Split) Octonionic Multiplication and its Extension to the Cayley--Dickson Tower |
| topic | Rings and Algebras 81R12, 11R52, 17A01 |
| url | https://arxiv.org/abs/2512.22134 |