A sedenion algebraic representation of three colored fermion generations

Niels Gresnigt*

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review


Three generations of fermions with SU(3) C symmetry are represented algebraically in terms of the algebra of sedenions, S, generated from the octonions, O, via the Cayley-Dickson process. Despite significant recent progress in generating the Standard Model gauge groups and particle multiplets from the four normed division algebras, an algebraic motivation for the existence of exactly three generations has been difficult to substantiate. In the sedenion model, one generation of leptons and quarks with SU(3) C symmetry is represented in terms of two minimal left ideals of C l(6), generated from a subset of all left actions of the complex sedenions on themselves. Subsequently, the finite group S 3, which are automorphisms of S but not of O, is used to generate two additional generations. The present paper highlight the key aspects and ideas underlying this construction.

Original languageEnglish
Article number012061
JournalJournal of Physics: Conference Series
Issue number1
Publication statusPublished - 2023
Externally publishedYes
Event12th International Symposium on Quantum Theory and Symmetries, QTS 2023 - Prague, Czech Republic
Duration: 24 Jul 202328 Jul 2023


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