  We extend the Lagrangian formulation of relativistic non-abelian fluids in
group theory language. We propose a Mathisson-Papapetrou equation for spinning
fluids in terms of the reduction limit of de Sitter group. The equation we find
correctly boils down to the one for non-spinning fluids. We study the
application of our results for an FRW cosmological background for fluids with
no vorticity and for dusts in the vicinity of a Kerr black hole. We also
explore two alternative approaches based on a group theoretical formulation of
particles dynamics.
