Sedenions, the Clifford algebra $\mathbb{C}l(8)$, and three fermion generations

Gresnigt, Niels G.

doi:10.22323/1.364.0615

Cited by 2 publications

(1 citation statement)

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“…The connection between C (6) and C (4), with a topological representation of leptons and quarks in terms of 3-belts is therefore essentially unique. This is interesting because these Clifford algebras (and others) can be generated from the left and right actions of the octonions and quaternions on themselves respectively (or tensor products of division algebras acting on themselves) [5,[20][21][22].…”

Section: Discussionmentioning

confidence: 99%

Topological preons from algebraic spinors

Gresnigt

2021

Eur. Phys. J. C

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It is demonstrated that many of the assumed rules that govern the structure of a previously proposed topological preon model, in which simple non-trivial braids consisting of three twisted ribbons are mapped to the first generation of leptons and quarks, are automatically adhered to when the algebraic spinors of two complex Clifford algebras are identified with braids via a suitable map. Much of the assumed topological architecture of this model can therefore be interpreted as a direct consequence of the deeper algebraic structures upon which the minimal ideals of these Clifford algebras are constructed. This result deepens the understanding of how these two complementary descriptions, one topological and one algebraic, of Standard Model symmetries are intimately connected despite originating from very different perspectives.

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Section: Discussionmentioning

confidence: 99%