Pure spinor cohomology is related to the Lie algebra cohomology of some infinite-dimensional Lie superalgebra
So, we have to first define that infinite-dimensional Lie superalgebra. The definition is motivated by the super-Yang-Mills theory, and the resulting algebra is called SYM.
Let us proceed to its definition.
This is an infinite-dimensional algebra. Moreover, this is actually a quadratic algebra, because the constraint (7) is quadratic in generators.