Let $(E,[,],\varphi )$ be a Lie fiber bundle (defined in last messages). I define a differential over the exterior forms $\Lambda^* (E)$:

$$df(s)= \varphi (s)(f)$$

$$d\alpha (s,s')= \varphi (s).\alpha (s')- \varphi (s').\alpha (s)- \alpha ([s,s'])$$

for $\alpha \in \Lambda^1 (E)$, and $f$ a smooth function. We then have:

$$d^2=0$$

If $\varphi ([s,s'])=[\varphi (s), \varphi (s')]$.

The Lie cohomology is the cohomology of the so defined complex $H^*_L (E,{\bf R})$.

Can we define invariants of the Lie fiber bundle?