TY - JOUR

T1 - Sedenions, the Clifford algebra C`(8), and three fermion generations

AU - Gresnigt, Niels G.

N1 - Publisher Copyright:
© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0).

PY - 2019

Y1 - 2019

N2 - Recently there has been renewed interest in using tensor products of division algebras, together with their associated Clifford algebras, to identify the structures of the Standard Model. One full generations of leptons and quarks transforming correctly under the electrocolor group SU(3)c U(1)em can be described in terms of complex octonion algebra C O. By going beyond the division algebras, and considering the larger Cayley-Dickson algebra of sedenions S, this one generation model is extended to exactly three generations. Each generation is contained in an C O subalgebra of C S, however these three subalgebras are not independent of one another. This three generation model can be related to an alternative model of three generations based on the exceptional Jordan algebra J3(O). It is speculated that the shared C H algebra common to all three generations might form a basis for CKM mixing.

AB - Recently there has been renewed interest in using tensor products of division algebras, together with their associated Clifford algebras, to identify the structures of the Standard Model. One full generations of leptons and quarks transforming correctly under the electrocolor group SU(3)c U(1)em can be described in terms of complex octonion algebra C O. By going beyond the division algebras, and considering the larger Cayley-Dickson algebra of sedenions S, this one generation model is extended to exactly three generations. Each generation is contained in an C O subalgebra of C S, however these three subalgebras are not independent of one another. This three generation model can be related to an alternative model of three generations based on the exceptional Jordan algebra J3(O). It is speculated that the shared C H algebra common to all three generations might form a basis for CKM mixing.

UR - http://www.scopus.com/inward/record.url?scp=85098915502&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:85098915502

SN - 1824-8039

VL - 364

JO - Proceedings of Science

JF - Proceedings of Science

M1 - 615

T2 - 2019 European Physical Society Conference on High Energy Physics, EPS-HEP 2019

Y2 - 10 July 2019 through 17 July 2019

ER -