How to find the balanced reaction equation for the decomposition of potassium dichromate in non aqueous conditions? I can't find a method to balance a reaction: the heating of potassium dichromate, which forms potassium dichromate (III), dichromate oxide (III) and oxygen. 
I can't add water products as $\ce{H+}$, $\ce{{}^{-}OH}$ because we are not in solution. 
So, how can I balance it? 

Who oxidises in this redox? The oxygen inside the salt? The oxygen of $\ce{H2O}$ which is in the air?
I think that part of your difficulty lies in incorrect naming of the products which are simply potassium chromate(VI) and chromium(III) oxide together with oxygen. The equation then becomes:

$$\ce {4K2Cr2O7 -&gt; 4K2CrO4 + 2Cr2O3 + 3O2}$$

As for what is oxidized and reduced; the chromium is reduced from chromium(VI) to chromium(III) in going from $\ce{K2Cr2O7}$ to $\ce{Cr2O3}$ and some of the oxygen is oxidized from −2 in the dichromate to 0 in the oxygen gas.