  We provide a necessary and sufficient condition for the consistency of the
supertrace, through the existence of a certain ground state projector. We build
this projector and check its properties to the first two orders in the number
operator and to all orders in the deformation parameter. We then find the
relation between the gravitational and internal gauge couplings in the
resulting unified three-dimensional Chern--Simons theory for Blencowe--Vasiliev
higher spin gravity coupled to fractional spin fields and internal gauge
potentials. We also examine the model for integer or half-integer fractional
spins, where infinite dimensional ideals arise and decouple, leaving finite
dimensional gauge algebras $gl(2l+1)$ or $gl(l|l+1)$ and various real forms
thereof.
