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Cartan lemma

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If for linear forms , , in variables the sum of the exterior products vanishes

and if the are linearly independent, then the are linear combinations of the with symmetric coefficients:

Proved by E. Cartan in 1899.

References

[1] E. Cartan, "Les systèmes différentielles extérieurs et leur applications géométriques" , Hermann (1945)


Comments

The original paper containing this result is [a1].

References

[a1] E. Cartan, "Sur certaines expressions différentielles et le problème de Pfaff" Ann. Ec. Norm. (3) , 16 (1899) pp. 239–332
How to Cite This Entry:
Cartan lemma. M.I. Voitsekhovskii (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Cartan_lemma&oldid=12449
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098