Real semisimple Lie groups and balanced metrics

Given any non-compact real simple Lie group G_o of inner type and even dimension, we prove the existence of an invariant complex structure J and a Hermitian balanced metric on G_o and on any compact quotient M= Gamma/G_o, with Gamma a cocompact lattice. We also prove that (M,J) does not carry any pluriclosed metric, in contrast to the case of even dimensional compact Lie groups, which admit pluriclosed but not balanced metrics.