Sedenion

The sedenion number system is an extension of the octonions of mathematics. It was first mentioned by American mathematician James Joseph Sylvester in 1884. Some 21st-century research in particle physics has made use of sedenions.

Quotes

• In January 1844, Graves sent three letters to Hamilton expanding on his discovery. He considered the idea of a general theory of ‘2^m-ions’, and tried to construct a 16-dimensional normed division algebra, but he “met with an unexpected hitch” and came to doubt that this was possible.
  • John C. Baez (2002) . "The octonions". Bull. Amer. Math. Soc. 39: 145–205. (p. 146)

• The sedenions should not be ruled out as playing a role in particle physics on the basis that they do not constitute a division algebra.
  • Adam B. Gillard, Niels G. Gresnigt (2019) . "Three fermion generations with two unbroken gauge symmetries from the complex sedenions". The European Physical Journal C 79 (5): 1–11 (446). DOI:10.1140/epjc/s10052-019-6967-1. (p. 8)

• Beyond the sedenions, one might not expect new physics. ... The fundamental symmetries remain those of the octonions, with only additional factors of the permutation group S₃ being added.
  • Adam B. Gillard, Niels G. Gresnigt (2019) . "Three fermion generations with two unbroken gauge symmetries from the complex sedenions". The European Physical Journal C 79 (5): 1–11 (446). DOI:10.1140/epjc/s10052-019-6967-1. (p. 8)

• We motivate $\mathbb {S}$ as a natural algebraic candidate to describe three generations, and argue that Cayley–Dickson algebras beyond the sedenions are unlikely to offer additional physical insights.
  • N. G. Gresnigta, L. Gourlaya, A. Varmaa (2023) "Toward a Three Generation Model of Standard Model Fermions Based on Cayley–Dickson Sedenions". Physics of Particles and Nuclei 54 (6): 1006–1010. ISSN 1063-7796. DOI:10.1134/S1063779623060138. (p. 1006)

• We propose that the Cayley–Dickson algebra of sedenions, generated from $\mathbb {O}$, constitutes a natural algebraic candidate that can be used to extend the existing models from a single generation to three.
  • N. G. Gresnigta, L. Gourlaya, A. Varmaa (2023) "Toward a Three Generation Model of Standard Model Fermions Based on Cayley–Dickson Sedenions". Physics of Particles and Nuclei 54 (6): 1006–1010. ISSN 1063-7796. DOI:10.1134/S1063779623060138. (p. 1006)

See also

• William Rowan Hamilton
• History of mathematics
• Mathematics
• Quaternion
• Octonion