On the rational homotopy Lie algebra of spaces with finite dimensional rational cohomology and homotopy
Annales de l'Institut Fourier, Tome 39 (1989) no. 1, pp. 193-206.

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.

@article{AIF_1989__39_1_193_0,
     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},
     pages = {193--206},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {39},
     number = {1},
     year = {1989},
     doi = {10.5802/aif.1163},
     mrnumber = {90h:55018},
     zbl = {0657.55016},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1163/}
}
TY  - JOUR
AU  - Markl, Martin
TI  - On the rational homotopy Lie algebra of spaces with finite dimensional rational cohomology and homotopy
JO  - Annales de l'Institut Fourier
PY  - 1989
SP  - 193
EP  - 206
VL  - 39
IS  - 1
PB  - Institut Fourier
PP  - Grenoble
UR  - http://www.numdam.org/articles/10.5802/aif.1163/
DO  - 10.5802/aif.1163
LA  - en
ID  - AIF_1989__39_1_193_0
ER  - 
%0 Journal Article
%A Markl, Martin
%T On the rational homotopy Lie algebra of spaces with finite dimensional rational cohomology and homotopy
%J Annales de l'Institut Fourier
%D 1989
%P 193-206
%V 39
%N 1
%I Institut Fourier
%C Grenoble
%U http://www.numdam.org/articles/10.5802/aif.1163/
%R 10.5802/aif.1163
%G en
%F 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) no. 1, pp. 193-206. doi : 10.5802/aif.1163. http://www.numdam.org/articles/10.5802/aif.1163/

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

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

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

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

[5] S. Halperin, The structure of π * ( Ω S ) , Astérisque, 113-114, 109-117. | Numdam | MR | Zbl

[6] R. Hartshorne, Algebraic geometry, Springer, 1977. | MR | Zbl

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

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

[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

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

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

Cité par Sources :