  In this article we investigate the application of complex split biquaternions
and bioctonions to the standard model. We show that the Clifford algebras Cl(3)
and Cl(7) can be used for making left-right symmetric fermions. Hence we
incorporate right-handed neutrinos in the division algebras based approach to
the standard model. The right-handed neutrinos, also known as sterile
neutrinos, are a potential dark-matter candidate. We discuss the left-right
symmetric fermions and their phenomenology using the division algebra approach.
We describe the gauge groups associated with the left-right symmetric model and
prospects for unification through division algebras. We investigate the
possibility of obtaining three generations of fermions and charge/mass ratios
through the exceptional Jordan algebra $J_3(O)$ and the exceptional groups
$F_4$ and $E_6$.
