Separated Lie models and the homotopy Lie algebra
نویسندگان
چکیده
منابع مشابه
Separated Lie Models and the Homotopy Lie Algebra
A simply connected topological space X has homotopy Lie algebra ( X) Q. Following Quillen, there is a connected di erential graded free Lie algebra (dgL) called a Lie model, which determines the rational homotopy type of X , and whose homology is isomorphic to the homotopy Lie algebra. We show that such a Lie model can be replaced with one that has a special property we call separated. The homo...
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Given a space X let LX denote its rational homotopy Lie algebra π∗(ΩX) ⊗ Q. A cell attachment f : ∨iSi → X is said to be free if the Lie ideal in LX generated by f is a free Lie algebra. This condition is shown to be general in the following sense. Given a space X with rational cone length N , then X is rationally homotopy equivalent to a space constructed using at most N + 1 free cell attachme...
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Let A be a graded-commutative, connected k-algebra generated in degree 1. The homotopy Lie algebra gA is defined to be the Lie algebra of primitives of the Yoneda algebra, ExtA(k, k). Under certain homological assumptions on A and its quadratic closure, we express gA as a semi-direct product of the well-understood holonomy Lie algebra hA with a certain hA-module. This allows us to compute the h...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2008
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2007.05.018