Let R be a subring ring of Q. We reserve the symbol p for the least prime which is not a unit in R; if R ⊒Q, then p=∞. Denote by DGL nnp, n≥1, the category of (n-1)-connected np-dimensional differential graded free Lie algebras over R. In [1] D. Anick has shown that there is a reasonable concept of homotopy in the category DGL nnp. In this work we intend to answer the following two questions: Given an object (L(V), ϖ) in DGL n3n+2 and denote by S(L(V), ϖ) the class of objects homotopy equivalent to (L(V), ϖ). How we can characterize a free dgl to belong to S(L(V), ϖ)? Fix an object (L(V), ϖ) in DGL n3n+2. How many homotopy equivalence classes of objects (L(W), δ) in DGL n3n+2 such that H * (W, d′)≊H * (V, d) are there? Note that DGL n3n+2 is a subcategory of DGL nnp when p>3. Our tool to address this problem is the exact sequence of Whitehead associated with a free dgl.
@article{bwmeta1.element.doi-10_2478_BF02475655,
author = {Mahmoud Benkhalifa and Nabilah Abughzalah},
title = {On the homotopy type of (n-1)-connected (3n+1)-dimensional free chain Lie algebra},
journal = {Open Mathematics},
volume = {3},
year = {2005},
pages = {58-75},
zbl = {1070.55011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475655}
}
Mahmoud Benkhalifa; Nabilah Abughzalah. On the homotopy type of (n-1)-connected (3n+1)-dimensional free chain Lie algebra. Open Mathematics, Tome 3 (2005) pp. 58-75. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475655/
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