  Let G be a discrete group. Suppose that the reduced group C*-algebra of G is
simple. We use results of Kalantar-Kennedy and Haagerup, and Banach space
interpolation, to prove that, for p in (1,infinity), the reduced group L^p
operator algebra F^p_r(G) and its *-analog B^{p,*}_r(G) are simple. If G is
countable, we prove that the Banach algebras generated by the left regular
representations on reflexive Orlicz sequence spaces and certain Lorentz
sequence spaces are also simple. We prove analogous results with simplicity
replaced by the unique trace property. For use in the Orlicz sequence space
case, we prove that if p is in (1,infinity), then any reflexive Orlicz sequence
space is isomorphic (not necessarily isometrically) to a space gotten by
interpolation between l^p and some other Orlicz sequence space.
