On the rational homotopy Lie algebra of spaces with finite dimensional rational cohomology and homotopy

Martin Markl

Annales de l'institut Fourier (1989)

  • Volume: 39, Issue: 1, page 193-206
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Markl, Martin. "On the rational homotopy Lie algebra of spaces with finite dimensional rational cohomology and homotopy." Annales de l'institut Fourier 39.1 (1989): 193-206. <http://eudml.org/doc/74824>.

@article{Markl1989,
abstract = {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.},
author = {Markl, Martin},
journal = {Annales de l'institut Fourier},
keywords = {finite dimensional rational graded Lie algebras; rational homotopy Lie algebra; structure constants of graded Lie algebras; strong arithmetic condition; space of type F; minimal model},
language = {eng},
number = {1},
pages = {193-206},
publisher = {Association des Annales de l'Institut Fourier},
title = {On the rational homotopy Lie algebra of spaces with finite dimensional rational cohomology and homotopy},
url = {http://eudml.org/doc/74824},
volume = {39},
year = {1989},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 39
IS - 1
SP - 193
EP - 206
AB - 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.
LA - eng
KW - finite dimensional rational graded Lie algebras; rational homotopy Lie algebra; structure constants of graded Lie algebras; strong arithmetic condition; space of type F; minimal model
UR - http://eudml.org/doc/74824
ER -

References

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  1. [1] A. BOREL, Linear algebraic groups, W.A. Benjamin, New-York, 1969. Zbl0186.33201MR40 #4273
  2. [2] J.-B. FRIEDLANDER, S. HALPERIN, An arithmetic characterization of the rational homotopy groups of certain spaces, Inv. Math., 53 (1979), 117-133. Zbl0396.55010MR81f:55006b
  3. [3] S. HALPERIN, Finiteness in the minimal models of Sullivan, Trans. Amer. Math. Soc., 230 (1977), 173-199. Zbl0364.55014MR57 #1493
  4. [4] S. HALPERIN, Spaces whose rational homology and ѱ-homotopy are both finite dimensional, Astérisque, 113-114 (1984), 198-205. Zbl0546.55015MR86a:55015
  5. [5] S. HALPERIN, The structure of π*(ΩS), Astérisque, 113-114, 109-117. Zbl0546.55014MR86b:55009
  6. [6] R. HARTSHORNE, Algebraic geometry, Springer, 1977. Zbl0367.14001MR57 #3116
  7. [7] J.-M. LEMAIRE, F. SIGRIST, Dénombrement de types d'homotopie rationnelle, C.R. Acad. Paris, Sér. A, 287 (1978), 109-112. Zbl0382.55005MR80b:55009
  8. [8] D. QUILLEN, Rational homotopy theory, Ann. Math., 90 (1969), 205-295. Zbl0191.53702MR41 #2678
  9. [9] P. SAMUEL, O. ZARISKI, Commutative algebra, Vol. I, Princeton N.J., Van Nostrand, 1958. 
  10. [10] P. SAMUEL, O. ZARISKI, Commutative algebra, Vol. II, Princeton N.J., Van Nostrand, 1960. Zbl0121.27801
  11. [11] I.-R. SHAFAREVICH, Osnovy algebraicheskoj geometrii, Moskva, 1972. Zbl0258.14001
  12. [12] D. TANRÉ, Homotopie rationnelle : Modèles de Chen, Quillen, Sullivan, Lecture Notes in Math. 1025, Springer, 1983. Zbl0539.55001MR86b:55010

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