词条 | Milnor–Moore theorem |
释义 |
In algebra, the Milnor–Moore theorem, introduced in {{harv|Milnor|Moore|1965}}, states: given a connected graded cocommutative Hopf algebra A over a field of characteristic zero with , the natural Hopf algebra homomorphism from the universal enveloping algebra of the "graded" Lie algebra of primitive elements of A to A is an isomorphism. (The universal enveloping algebra of a graded Lie algebra L is the quotient of the tensor algebra of L by the two-sided ideal generated by elements xy-yx - (-1)|x||y|[x, y].) In topology, the term usually refers to the corollary of the result explained above that for a simply connected space X, it holds true that compare,[1] theorem 21.5 This work may also be compared with that by E. Halpern [1958] listed below. References1. ^Y. Felix, S. Halperin, J.-C. Thomas, "Rational Homotopy theory", Springer 2001.
External links
2 : Theorems in abstract algebra|Hopf algebras |
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