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geometry > differential geometry > differential form > polynomial differential form

... > abstract algebra > algebraic structure > associative algebra > differential graded algebra > polynomial differential form

algebra > differential algebra > differential graded algebra > polynomial differential form

... > abstract algebra > algebraic structure > homological algebra > differential graded algebra > polynomial differential form

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polynomial differential form

In algebra, the ring of polynomial differential forms on the standard n-simplex is the differential graded algebra:

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

Varying n, it determines the simplicial commutative dg algebra:

${\\displaystyle \\Omega _{\ ext{poly}}^{*}}$

(each ${\\displaystyle u:\ o }$ induces the map ${\\displaystyle \\Omega _{\ ext{poly}}^{*}()\ o \\Omega _{\ ext{poly}}^{*}(),t_{i}\\mapsto \\sum _{u(j)=i}t_{j}}$ ).
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Polynomial_differential_form)

forme différentielle polynomiale

French

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http://data.loterre.fr/ark:/67375/PSR-QBPHV79Q-6

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