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A factorization of the homology of a differential graded Lie algebra

✍ Scribed by Jonathan A. Scott

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
133 KB
Volume
167
Category
Article
ISSN
0022-4049

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✦ Synopsis

Let (L; @) be a di erential graded Lie algebra over the prime ΓΏeld Fp. There exists an isomorphism of Hopf algebras H * (UL) ∼ = UE, where E is a graded Lie algebra (J. Pure. Appl. Algebra 83 (1992) 237-282). Suppose that L is q-reduced for some q ΒΏ 1. We prove a generalization of a classical theorem of Sullivan (Inst. Hautes Γƒ Etudes Sci. Publ. Math. (47) (1977) 269 -331), which we use to show that there is an isomorphism of graded Lie algebras H (L; @) ∼ = E Γ— K, where K is an abelian (qp + p -2)-reduced ideal. As a consequence, if X is a ΓΏnite, q-connected, n-dimensional CW complex, and EX is its mod p homotopy Lie algebra (J. Pure. Appl.

πŸ“œ SIMILAR VOLUMES

On the homology of graded Lie algebras
On the homology of graded Lie algebras
✍ Paulo Tirao πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 101 KB

We consider the homology of ΓΏnite-dimensional-graded Lie algebras with coe cients in a ΓΏnite-dimensional-graded module. By a combinatorial approach we give a lower bound for their total homology. Our result extends a result of Deninger and Singhof for the case of trivial coe cients. Applications for