A differential kform of degree in an exterior algebra is decomposable if there exist oneforms such that
(1)

where denotes a wedge product. Forms of degree 0, 1, , and are always decomposable. Hence the first instance of indecomposable forms occurs in , in which case is indecomposable.
If a form has a form envelope of dimension then it is decomposable. In fact, the oneforms in the (dual) basis to the envelope can be used as the above.
Plücker's equations form a system of quadratic equations on the in
(2)

which is equivalent to being decomposable. Since a decomposable form corresponds to a dimensional subspace, these quadratic equations show that the Grassmannian is a projective algebraic variety. In particular, is decomposable if for every ,
(3)

where denotes tensor contraction and is the dual vector space to .