Algebraic characterizations of the algebra of functions and of the Lie algebra of vector fields of a manifold
Compositio Mathematica, Tome 45 (1982) no. 2, pp. 199-205. 
@article{CM_1982__45_2_199_0,
     author = {De Wilde, M. and Lecomte, P.},
     title = {Algebraic characterizations of the algebra of functions and of the {Lie} algebra of vector fields of a manifold},
     journal = {Compositio Mathematica},
     pages = {199--205},
     publisher = {Martinus Nijhoff Publishers},
     volume = {45},
     number = {2},
     year = {1982},
     mrnumber = {651981},
     zbl = {0503.58038},
     language = {en},
     url = {http://archive.numdam.org/item/CM_1982__45_2_199_0/}
}
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De Wilde, M.; Lecomte, P. Algebraic characterizations of the algebra of functions and of the Lie algebra of vector fields of a manifold. Compositio Mathematica, Tome 45 (1982) no. 2, pp. 199-205. http://archive.numdam.org/item/CM_1982__45_2_199_0/

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[3] R. Palais: Natural operations on differential forms. Trans. A.M.S. 92 (1959), 125-141. | MR | Zbl

[4] S. Van Strien: Unicity of the Lie Product. Comp. Math. 40 (1980), 79-85. | EuDML | Numdam | MR | Zbl