The Radical of the Homotopy Lie Algebra

DOI10.2307/2374504zbMath0654.55011OpenAlexW1979422900WikidataQ115228806 ScholiaQ115228806MaRDI QIDQ3800747

Yves Félix, Jean-Claude Thomas, Carl Jacobsson, Clas Löfwall, Stephen Halperin

Publication date: 1988

Published in: American Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2374504

zbMATH Keywords

depthglobal dimensionLyusternik-Schnirelman categorynoetherian local ringhomology of the Koszul complexhomotopy Lie algebras of spaces and local ringsminimal models of a spaceradical of the homotopy Lie algebras

Mathematics Subject Classification ID

Rational homotopy theory (55P62) Graded Lie (super)algebras (17B70) Local rings and semilocal rings (13H99)

Related Items (33)

Graded Lie algebras with finite polydepth ⋮ Stable cohomology over local rings ⋮ The ranks of the homotopy groups of a space of finite LS category ⋮ On Hilali's conjecture related to Halperin's ⋮ Exponential growth and an asymptotic formula for the ranks of homotopy groups of a finite 1-connected complex ⋮ An asymptotic formula for the ranks of homotopy groups ⋮ Malcev completions, LS category, and depth ⋮ Mod \(p\) loop space homology ⋮ A remarkable property of the (co) syzygy modules of the residue field of a nonregular local ring ⋮ The free loop space equivariant cohomology algebra of some formal spaces ⋮ LS category of classifying spaces and 2-cones ⋮ Complete intersection dimension ⋮ The homotopy Lie algebra of a Tor-independent tensor product ⋮ Bounds on cohomological support varieties ⋮ Density and unique decomposition theorems for the lattice of cellular classes ⋮ The depth and LS category of a topological space ⋮ Engel elements in the homotopy Lie algebra ⋮ Separated Lie models and the homotopy Lie algebra ⋮ A computer-aided study of the graded Lie algebra of a local commutative noetherian ring. -- Appendix A: Some technical details about how the computer was used. -- Appendix B (by Clas Löfwall): The Lie algebra structure of a ring satisfying \({\mathcal M}_ 3\) and variants ⋮ A counter-example to a conjecture of Félix ⋮ Universal enveloping algebras and loop space homology ⋮ Le complexe de Koszul en algèbre et topologie. (The Koszul complex in algebra and topology) ⋮ Graded Lie algebras of depth one ⋮ The category of a map and the grade of a module ⋮ Effet d'un attachement cellulaire dans l'homologie de l'espace des lacets. (The effect of attaching cells to the homology of loop spaces) ⋮ Cohomology over fiber products of local rings ⋮ Finite CW complexes with maximal torsion gaps ⋮ Category, growth and grade in a fibration ⋮ Vasconcelos' conjecture on the conormal module ⋮ Dimension globale et classe fondamentale d'un espace. (Global dimension and fundamental class of a space.) ⋮ Rational Lusternik-Schnirelmann category of fibrations ⋮ Central elements and deformations of local rings ⋮ The evaluation map of some Gorenstein algebras

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