algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...

, the ring of polynomial differential forms on the standard ''n''-simplex is the

differential graded algebra In mathematics – particularly in homological algebra, algebraic topology, and algebraic geometry – a differential graded algebra (or DGA, or DG algebra) is an algebraic structure often used to capture information about a topological or geo ...

: :

(\sum t_i - 1, \sum dt_i).

Varying ''n'', it determines the simplicial commutative dg algebra: :

\Omega^*_

(each

u: \to /math> induces the map \Omega^*_(\to \Omega^*_(, t_i \mapsto \sum_ t_j).

References

* Aldridge Bousfield and V. K. A. M. Gugenheim, §1 and §2 of: On PL De Rham Theory and Rational Homotopy Type, Memoirs of the A. M. S., vol. 179, 1976. *

External links

* https://ncatlab.org/nlab/show/differential+forms+on+simplices * https://mathoverflow.net/questions/220532/polynomial-differential-forms-on-bg Differential algebra Ring theory {{algebra-stub