On the rational homotopy Lie algebra of spaces with finite dimensional rational cohomology and homotopy
Markl, Martin
Annales de l'Institut Fourier, Tome 39 (1989), p. 193-206 / Harvested from Numdam
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On discute le problème de la caractérisation des algèbres de Lie graduées qui peuvent être réalisés comme des algèbres de Lie homotopiques d’espace de type F. Les résultats principaux sont exprimés à l’aide de la notion de variété des constantes structurales. On démontre aussi quelques critères pour des algèbres concrètes.

The problem of the characterization of graded Lie algebras which admit a realization as the homotopy Lie algebra of a space of type F is discussed. The central results are formulated in terms of varieties of structure constants, several criterions for concrete algebras are also deduced.

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     author = {Markl, Martin},
     title = {On the rational homotopy Lie algebra of spaces with finite dimensional rational cohomology and homotopy},
     journal = {Annales de l'Institut Fourier},
     volume = {39},
     year = {1989},
     pages = {193-206},
     doi = {10.5802/aif.1163},
     mrnumber = {90h:55018},
     zbl = {0657.55016},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1989__39_1_193_0}
}

Markl, Martin. On the rational homotopy Lie algebra of spaces with finite dimensional rational cohomology and homotopy. Annales de l'Institut Fourier, Tome 39 (1989) pp. 193-206. doi : 10.5802/aif.1163. http://gdmltest.u-ga.fr/item/AIF_1989__39_1_193_0/

[1] A. Borel, Linear algebraic groups, W.A. Benjamin, New-York, 1969. | MR 40 #4273 | Zbl 0186.33201

[2] J.-B. Friedlander, S. Halperin, An arithmetic characterization of the rational homotopy groups of certain spaces, Inv. Math., 53 (1979), 117-133. | MR 81f:55006b | Zbl 0396.55010

[3] S. Halperin, Finiteness in the minimal models of Sullivan, Trans. Amer. Math. Soc., 230 (1977), 173-199. | MR 57 #1493 | Zbl 0364.55014

[4] S. Halperin, Spaces whose rational homology and ѱ-homotopy are both finite dimensional, Astérisque, 113-114 (1984), 198-205. | MR 86a:55015 | Zbl 0546.55015

[5] S. Halperin, The structure of π*(ΩS), Astérisque, 113-114, 109-117. | MR 86b:55009 | Zbl 0546.55014

[6] R. Hartshorne, Algebraic geometry, Springer, 1977. | MR 57 #3116 | Zbl 0367.14001

[7] J.-M. Lemaire, F. Sigrist, Dénombrement de types d'homotopie rationnelle, C.R. Acad. Paris, Sér. A, 287 (1978), 109-112. | MR 80b:55009 | Zbl 0382.55005

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

[9] P. Samuel, O. Zariski, Commutative algebra, Vol. I, Princeton N.J., Van Nostrand, 1958.

[10] P. Samuel, O. Zariski, Commutative algebra, Vol. II, Princeton N.J., Van Nostrand, 1960. | Zbl 0121.27801

[11] I.-R. Shafarevich, Osnovy algebraicheskoj geometrii, Moskva, 1972. | Zbl 0258.14001

[12] D. Tanré, Homotopie rationnelle : Modèles de Chen, Quillen, Sullivan, Lecture Notes in Math. 1025, Springer, 1983. | MR 86b:55010 | Zbl 0539.55001