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The peculiar correlation effects on the triangular lattice are studied bymeans of the rotationally invariant slave boson method in a cellular clusterapproach. Hence nonlocal correlations are included in a short-range regime.Their impact for the single-band Hubbard model is studied at half filling,i.e., on the Mott transition, and with doping. Using the realistic bandstructure of Na$_x$CoO$_2$, we may also shed light on the cobaltate physics for$x$$\ge$1/3, with the in-plane transition from antiferromagnetic tendenciestowards the onset of ferromagnetism for a finite Hubbard $U$.

Correlation effects on the doped triangular lattice in view of the physics of sodium-rich Na$_x$CoO$_2$