Polinomning differentsial shakli - Polynomial differential form

Yilda algebra, halqasi polinomial differentsial shakllar standart bo'yicha n-sodda bo'ladi differentsial darajali algebra:^[1]

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

Turli xil n, bu belgilaydi sodda kommutativ dg algebra:

${ displaystyle Omega _ { text {poly}} ^ {*}}$

(har biri ${ displaystyle u: [n] dan [m]} gacha$ xaritani chiqaradi ${ displaystyle Omega _ { text {poly}} ^ {*} ([m]) to Omega _ { text {poly}} ^ {*} ([n]), t_ {i} mapsto sum _ {u (j) = i} t_ {j}}$).

Adabiyotlar

• Aldrij Bousfield va V. K. A. M. Gugenheim, §1 va §2: PLda De Rham nazariyasi va Ratsional gomotopiya turi, A. M. S. xotiralari, jild. 179, 1976 yil.
• Xinich, Vladimir (1997-02-11). "Gomotopiya algebralarining homologik algebrasi". arXiv:q-alg / 9702015.

Tashqi havolalar

• https://ncatlab.org/nlab/show/differential+forms+on+ simplices
• https://mathoverflow.net/questions/220532/polynomial-differential-forms-on-bg

Bu algebra bilan bog'liq maqola a naycha. Siz Vikipediyaga yordam berishingiz mumkin uni kengaytirish.