Consider a graded vector space with basis such that and . Now define a linear map (of degree 1) by and . It follows that d extends uniquely to a derivation .
The point of the example is to show that the derivation on is completely determined by its values on . So if i understand well, he considers a linear map of degree one defined by
(here is the set of elements of word length ) and
The first question that i'm stuck on is for , i mean is of length , how it can be in .