  A monolayer of $MoS_{2}$ has a non-centrosymmetric crystal structure, with
spin polarized bands. It is a two valley semiconductor with direct gap falling
in the visible range of the electromagnetic spectrum. Its optical properties
are of particular interest in relation to valleytronics and possible device
applications. We study the longitudinal and the transverse Hall dynamical
conductivity which is decomposed into charge, spin and valley contributions.
Circular polarized light associated with each of the two valleys separately is
considered and results are filtered according to spin polarization. Temperature
can greatly change the spin admixture seen in the frequency window where they
are not closely in balance.
