Polynomial differential form

In algebra, for a non-negative integer n, the ring of polynomial differential forms on the standard n-simplex Δ^{n is the differential graded algebra:}

$\Omega _{\text{poly}}^{*}(\Delta ^{n})=\mathbb {Q} [t_{0},...,t_{n},dt_{0},...,dt_{n}]/(\sum t_{i}-1,\sum t_{i})$

Varing n, it determines the simplicial commutative dg algebra:

$\Omega _{\text{poly}}^{*}.$

References

• Hinich, Vladimir (1997-02-11). "Homological algebra of homotopy algebras". arXiv:q-alg/9702015.

External links

• https://ncatlab.org/nlab/show/differential+forms+on+simplices