nLab decomposable differential form

Definition

A differential form $\omega \in \Omega^n$ of homogeneous degree $n$ is said to be decomposable if it is the wedge product of $n$ differential 1-form $(\alpha_k \in \Omega^1)_{k \in \{1, \cdots, n\}}$:

$$\omega = \alpha_1 \wedge \alpha_2 \wedge \cdots \wedge \alpha_n$$

More generally in an $\mathbb{N}$-graded-commutative algebra an element of homogeneous degree may be called decomposable if it may be written as the product of elements of degree 1.

Related concepts

• decomposable tensor

• H-cohomology

References

See also

• MathWorld, Decomposable