Polynomial differential form
 | The topic of this article may not meet Wikipedia's general notability guideline. (October 2019) |
 | This article may be too technical for most readers to understand. (October 2019) |
In algebra, the ring of polynomial differential forms on the standard n-simplex is the differential graded algebra:[1]
![{\displaystyle \Omega _{\text{poly}}^{*}([n])=\mathbb {Q} [t_{0},...,t_{n},dt_{0},...,dt_{n}]/(\sum t_{i}-1,\sum t_{i}).}](/media/api/rest_v1/media/math/render/svg/29923d34afd6c004520393d8c038f292f64b2096)
Varing n, it determines the simplicial commutative dg algebra:
(each induces the map ).
![{\displaystyle u:[n]\to [m]}](/media/api/rest_v1/media/math/render/svg/a39fd8924b9cb09430e0cc1161803300fe55a2b5)
![{\displaystyle \Omega _{\text{poly}}^{*}([m])\to \Omega _{\text{poly}}^{*}([n]),t_{i}\mapsto \sum _{u(j)=i}t_{j}}](/media/api/rest_v1/media/math/render/svg/3d60e3ec6f36c3f7bdc8bec9c08cf236e21bcabe)
References
- Hinich, Vladimir (1997-02-11). "Homological algebra of homotopy algebras". arXiv:q-alg/9702015.
External links
 | This algebra-related article is a stub. You can help Wikipedia by expanding it. |