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 ‘2m-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 http://doi.org/10.1090/S0273-0979-01-00934-X The octonions Bull. Amer. Math. Soc. 39 145–205 2002 (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 Guillard Adam B. Gresnigt Niels G. Three fermion generations with two unbroken gauge symmetries from the complex sedenions https://link.springer.com/article/10.1140/epjc/s10052-019-6967-1 The European Physical Journal C Springer 79 5 2019 1–11 (446) 10.1140/epjc/s10052-019-6967-1 free 2019EPJC...79..446G 102351250 1904.03186 (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 Guillard Adam B. Gresnigt Niels G. Three fermion generations with two unbroken gauge symmetries from the complex sedenions https://link.springer.com/article/10.1140/epjc/s10052-019-6967-1 The European Physical Journal C Springer 79 5 2019 1–11 (446) 10.1140/epjc/s10052-019-6967-1 free 2019EPJC...79..446G 102351250 1904.03186 (p. 8) We motivate 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 Gresnigt N. G. Gourlay L. Varma A. Toward a Three Generation Model of Standard Model Fermions Based on Cayley–Dickson Sedenions Physics of Particles and Nuclei 54 6 2023 1063-7796 10.1134/S1063779623060138 1006–1010 https://link.springer.com/10.1134/S1063779623060138 (p. 1006) We propose that the Cayley–Dickson algebra of sedenions, generated from , 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 Gresnigt N. G. Gourlay L. Varma A. Toward a Three Generation Model of Standard Model Fermions Based on Cayley–Dickson Sedenions Physics of Particles and Nuclei 54 6 2023 1063-7796 10.1134/S1063779623060138 1006–1010 https://link.springer.com/10.1134/S1063779623060138 (p. 1006) See also William Rowan Hamilton History of mathematics Mathematics Quaternion Octonion External links Category:Algebra Category:Numbers Category:Theoretical physics