The center of a graded connected Lie algebra is a nice ideal
(1996) Institut Fourier. Annales — Vol. 46, n° 1, p. 263-& (1996)
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- Let (L(V),d) be a free graded connected differential Lie algebra over the field Q of rational numbers. An ideal I in the Lie algebra H(L(V),d) is called nice if, for every cycle alpha is an element of L(V) such that [alpha] belongs to I, the kernel of the map H(L(V),d) --> H(L(V + Qx),d), d(x) = alpha, is contained in I. We show that the center of H(L(V),d) is a nice ideal and we give in that case some informations on the structure of the Lie algebra H(L(V + Qx),d). We apply this computation for the determination of the rational homotopy Lie algebra L(X) = pi*(Omega X) X Q of a simply connected space X. We deduce that the kernel of the map L(X) --> L(Y) induced by the attachment of a cell along an element in the center is contained in the center.
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Félix, Y. (1996). The center of a graded connected Lie algebra is a nice ideal. Institut Fourier. Annales, 46(1), 263-&. https://hdl.handle.net/2078.5/41934 (Original work published 1996)