How can carbon dioxide be converted into carbon and oxygen?
In my opinion, the catalytic, solar-driven conversion of carbon dioxide to methanol, formic acid, etc. is much more interesting and promising, but since Enrico asked for the conversion of carbon dioxide to carbon itself:

The group around Yutaka Tamaura was/is active in this field. In one of their earlier publications,[1] they heated magnetite ($\ce{Fe3O4}$) at 290 °C for 4 hours in a stream of hydrogen to yield a material which turned out to be stable at room temperature under nitrogen. This material, $\ce{Fe_{3+\delta}O4}$ $(\delta=0.127)$, i.e. the metastable cation-excess magnetite is able to incorporate oxygen in the form of $\ce{O^2-}$. 

Under a $\ce{CO2}$ atmosphere, the oxygen-deficient material converted to "ordinary" $\ce{Fe3O4}$ with carbon deposited on the surface.

This remarkable reaction however is not catalytic, but a short recherche showed that the authors have published a tad more in this field. Maybe somebody else finds a a report on a catalytic conversion among their publications. 


Tamaura, Y.; Tahata, M. Complete reduction of carbon dioxide to carbon using cation-excess magnetite. Nature 1990, 346 (6281), 255–256. DOI: 10.1038/346255a0.