Topological preons from algebraic spinors

Abstract

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.

A sedenion algebraic representation of three colored fermion generations

“…More recent constructions have sought to extend these earlier results by describing additional SM structure in terms of tensor products of division algebras [2,3,4,5,6,7]. Many others have contributed to these, and related, algebraic approaches including those based on topology [8,9,10,11,12], exceptional Lie groups [13,14,15,16,17,18], Clifford algebras [19,20,21,22,23,24,25,26,27], and Jordan algebras [28,29,30,31,32,33].…”