Relative cohomologyConsider any representation of . It is also a representation of :is a representation of is a representation of

Indeed, let us remember the structure of the . The generators are:

The subalgebra is generated by . To have a representation of means to have operators , , , acting in the linear space .

We then define the action of in in terms of the action of :

This is consistent. In fact, there is an ideal such that

We defined so that .