Showing papers on "Differential graded Lie algebra published in 1989"
TL;DR: In this article, it was shown that the rational singular chain complex on a topological monoid is the enveloping algebra of a Lie algebra and that pth powers vanish in H * (QX; Zp) if A is generated as an R-algebra in dimensions below rp.
Abstract: Let (A, d) denote a free r-reduced differential graded R-algebra, where R is a commutative ring containing n for 1 a "diagonal" yi: A -+ A 0 A exists which satisfies the Hopf algebra axioms, including cocommutativity and coassociativity, up to homotopy. We show that (A, d) must equal U(L, 3) for some free differential graded Lie algebra (L, 6) This content downloaded from 157.55.39.203 on Sat, 27 Aug 2016 06:23:15 UTC All use subject to http://about.jstor.org/terms HOPF ALGEBRAS UP TO HOMOTOPY 453 if A is generated as an R-algebra in dimensions below rp . As a consequence, the rational singular chain complex on a topological monoid is seen to be the enveloping algebra of a Lie algebra. We also deduce, for an r-connected CW complex X of dimension enveloping algebra and that pth powers vanish in H* (QX; Zp) . DEPARTMENT OF MATHEMATICS, MASSACHUSETTS INSTITUTE OF TECHNOLOGY, CAMBRIDGE, MASSACHUSETTS 02139 This content downloaded from 157.55.39.203 on Sat, 27 Aug 2016 06:23:15 UTC All use subject to http://about.jstor.org/terms
105 citations