No I have actually never tried that on a math paper. But I will give it a try. Thank you!

Thanks for your comment. Do you know of any english reference for this?

I have a (possibly stupid) question about the paper. I wonder if there is a reason why the author uses quotients $\Gamma \backslash \widetilde{PSL}(2,\mathbb{R})$ instead of $\widetilde{SL}(2,\mathbb{R}) / \Gamma$?. The first thing I ask myself is, if both constructions yield isometric spaces (so does it matter if we take the left or right quotient)? And the second question is: is there any reason he writes $\widetilde{PSL}$ instead of $\widetilde{SL}$? As far as I know those to spaces are the same (since $SL$ covers $PSL$ two sheeted), but during the whole paper he writes $\widetilde{PSL}$.

Thank you. I will take a look at it. I have a question to your construction: Can we say anything about the signature of the PR-metric we obtain from the Killing form? In the case of $SL(2,\mathbb{R})$ it has signature $(2,1)$. Do all signatures appear?