Sur certaines algèbres de Lie de dérivations
Annales de l'Institut Fourier, Volume 32 (1982) no. 4, p. 143-150

Every c.d.g.a. with a Sullivan minimal model of finite type can be represented by a certain graded differential Lie algebra of derivations. This permits such a representation for the rational homotopy type of a topological space.

Il est démontré que toute a.d.g.c. ayant un modèle minimal de Sullivan de type fini peut être représentée par une certaine algèbre de Lie différentielle graduée de dérivations. En particulier on peut ainsi représenter le type d’homotopie rationnelle d’un espace topologique.

@article{AIF_1982__32_4_143_0,
     author = {F\'elix, Yves and Halperin, Stephen and Thomas, Jean-Claude},
     title = {Sur certaines alg\`ebres de Lie de d\'erivations},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {32},
     number = {4},
     year = {1982},
     pages = {143-150},
     doi = {10.5802/aif.897},
     zbl = {0487.55005},
     mrnumber = {84m:55011},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1982__32_4_143_0}
}

Félix, Yves; Halperin, Stephen; Thomas, Jean-Claude. Sur certaines algèbres de Lie de dérivations. Annales de l'Institut Fourier, Volume 32 (1982) no. 4, pp. 143-150. doi : 10.5802/aif.897. http://www.numdam.org/item/AIF_1982__32_4_143_0/

[1] P. Andrews and M. Arkowitz, Sullivan's minimal and higher order whitehead products, Can. J. of Math., XXX n° 5 (1978), 961-982. | MR 80b:55008 | Zbl 0441.55012

[2] H. J. Baues and J. M. Lemaire, Minimal models in homotopy theory, Math. Ann., 225 (1977), 219-242. | MR 55 #4174 | Zbl 0322.55019

[3] A. K. Bousfield and W.K.A.M. Gugenheim, On the PL de Rham theory and rational homotopy type, Memoirs of the A.M.S., 179 (1976). | Zbl 0338.55008

[4] S. Halperin, Lectures on minimal models, Preprint n° 111, Lille, 1977.

[5] D. Quillen, Rational homotopy theory, Ann. of Math., 90 (1969), 205-295. | MR 41 #2678 | Zbl 0191.53702

[6] G. Sjödin, Hopf algebras and derivations, J. of Algebra, 64 (1980), 218-229. | MR 84a:16016 | Zbl 0429.16008

[7] M. Schlessinger and J. D. Stasheff, Deformation theory and rational homotopy type, Preprint.

[8] D. Sullivan, Infinitesimal computations in topology, Publ. I.H.E.S., 47. | Numdam | Zbl 0374.57002

[9] D. Tanré, Modèle de Chen-Quillen-Sullivan, Thèse n° 535, Univ. des Sciences et Tech. de Lille I.