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

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.

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.

@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 = {https://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  - https://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 https://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, Volume 39 (1989) no. 1, pp. 193-206. doi : 10.5802/aif.1163. https://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

Cited by Sources: