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- Der Satz von Milnor-Moore, benannt nach John Milnor und John Moore, ist ein Lehrsatz aus dem mathematischen Gebiet der Theorie der Hopf-Algebren. Er stellt unter gewissen Voraussetzungen einen Zusammenhang zwischen einer solchen Hopf-Algebra und der in ihr enthaltenen Lie-Algebra der primitiven Elemente her. (de)
- In algebra, the Milnor–Moore theorem, introduced by John W. Milnor and John C. Moore classifies an important class of Hopf algebras, of the sort that often show up as cohomology rings in algebraic topology. The theorem states: given a connected, graded, cocommutative Hopf algebra A over a field of characteristic zero with for all n, 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. Here we say A is connected if is the field and for negative n. 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 all elements of the form . In algebraic topology, the term usually refers to the corollary of the aforementioned result, that for a pointed, simply connected space X, the following isomorphism holds: where denotes the loop space of X, compare with Theorem 21.5 from. This work may also be compared with that of (Halpern , ). (en)
- Inom matematiken är Milnor–Moores sats, introducerad av, ett resultat som säger att givet en sammanhängande graderad A över en kropp av karakteristik noll med är den naturliga Hopfalgebrahomomorfin från den universella envelopperande algebran av den "graderade" Liealgebran av av A till A är en isomorfi. (sv)
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- 3775 (xsd:nonNegativeInteger)
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- John C. (en)
- John W. (en)
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- Moore (en)
- Halpern (en)
- Milnor (en)
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- 1958 (xsd:integer)
- 1965 (xsd:integer)
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- Der Satz von Milnor-Moore, benannt nach John Milnor und John Moore, ist ein Lehrsatz aus dem mathematischen Gebiet der Theorie der Hopf-Algebren. Er stellt unter gewissen Voraussetzungen einen Zusammenhang zwischen einer solchen Hopf-Algebra und der in ihr enthaltenen Lie-Algebra der primitiven Elemente her. (de)
- Inom matematiken är Milnor–Moores sats, introducerad av, ett resultat som säger att givet en sammanhängande graderad A över en kropp av karakteristik noll med är den naturliga Hopfalgebrahomomorfin från den universella envelopperande algebran av den "graderade" Liealgebran av av A till A är en isomorfi. (sv)
- In algebra, the Milnor–Moore theorem, introduced by John W. Milnor and John C. Moore classifies an important class of Hopf algebras, of the sort that often show up as cohomology rings in algebraic topology. The theorem states: given a connected, graded, cocommutative Hopf algebra A over a field of characteristic zero with for all n, the natural Hopf algebra homomorphism In algebraic topology, the term usually refers to the corollary of the aforementioned result, that for a pointed, simply connected space X, the following isomorphism holds: (en)
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- Satz von Milnor-Moore (de)
- Milnor–Moore theorem (en)
- Milnor–Moores sats (sv)
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