  This paper represents a first attempt at unifying two promising models that
attempt to explain the origin of the internal symmetries of leptons and quarks.
It is shown that each of the four normed division algebras over the reals
admits a representation of a circular braid group. For the complex numbers and
the quaternions, the represented circular braid groups are $B_2$ and $B_3^c$,
precisely those used to construct leptons and quarks as framed braids in the
Helon model of Bilson-Thompson. It is then shown that these framed braids
coincide with the states that span the minimal left ideals of the complex
(chained) octonions, shown by Furey to describe one generation of leptons and
quarks with unbroken $SU(3)_{c}$ and $U(1)_{em}$ symmetry.
  The identification of basis states of minimal ideals with certain framed
braids is possible because the braiding in $B_2$ and $B_3^c$ in the Helon model
are interchangeable. It is shown that the framed braids in the Helon model can
be written as pure braid words in $B_3^c$ with trivial braiding in $B_2$,
something which is not possible for framed braids in general.

General Physics