  The Standard Model of particle physics provides very accurate predictions of
phenomena occurring at the sub-atomic level, but the reason for the choice of
symmetry group and the large number of particles considered elementary, is
still unknown. Along the lines of previous preon models positing a substructure
to explain these aspects, Bilson-Thompson showed how the first family of
elementary particles is realized as the crossings of braids made of three
strands, with charges resulting from twists of those strands with certain
conditions; in this topological model, there are only two distinct neutrino
states. Modeling the particles as braids implies these braids must be the
representation space of a Lie algebra, giving the symmetries of the Standard
Model. In this paper, this representation is made explicit, obtaining the
raising operators associated with the Lie algebra of $SU(5)$, one of the
earliest grand unified theories. Because the braids form a group, the action of
these operators are braids themselves, leading to their identification as gauge
bosons. Possible choices for the other two families are also given. Although
this realization of particles as braids is lacking a dynamical framework, it is
very suggestive, especially when considered as a natural method of adding
matter to loop quantum gravity.
