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Groupes et algèbres de Lie
Nicolas Bourbaki
- 01 Jan 1971
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TL;DR: Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements as mentioned in this paper.
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Abstract: Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements. Ce premier volume du Livre sur les Groupes et algebre de Lie, neuvieme Livre du traite, est consacre aux concepts fondamentaux pour les algebres de Lie. Il comprend les paragraphes: - 1 Definition des algebres de Lie; 2 Algebre enveloppante d une algebre de Lie; 3 Representations; 4 Algebres de Lie nilpotentes; 5 Algebres de Lie resolubles; 6 Algebres de Lie semi-simples; 7 Le theoreme d Ado. Ce volume est une reimpression de l edition de 1971."
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Citations
Hopf Algebras in Noncommutative Geometry
Joseph C. Várilly,Abdus Salam +1 more
- 01 Mar 2003
TL;DR: Hopf algebras have been used in many problems of noncommutative geometry, e.g., the Hopf algebra of rooted trees as discussed by the authors, which is an algebra of transverse differential operators introduced by Connes and Moscovici.
Long chains of topological group topologies—A continuation☆
W. Wistar Comfort,Dieter Remus +1 more
TL;DR: Theorem 3.4.3 as mentioned in this paper shows that the condition that a group contains a chain C with β = β is equivalent to a natural and purely set-theoretic condition, namely that the partially ordered set 〈 P (2 γ ), ⊆ 〉 contain a chain of length β.
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Primitive subalgebras of exceptional Lie algebras
TL;DR: Theorem 5.5.5 (p. 148) in the reductive case of Dynkin [2] is incorrect as discussed by the authors, in particular A3 0 Dδ, i 5 Θ Λ Θ 4 4 7 φ A1 in Es, A\ 0 Aγ in EΊ and Az 0 Ax in F4 are not maximal subalgebras.
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The Lie algebra associated to a unit form
TL;DR: In this article, a Lie algebra G˜(q)-an intersection matrix Lie algebra in the terminology of Slodowy by means of generalized Serre relations is associated to any unit form q(x)= ∑i=1nxi2+∑i
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•Posted Content
Residual $p$ properties of mapping class groups and surface groups
TL;DR: In this paper, it was shown that the mapping class group of a punctured oriented surface is conjugacy $p-separable and has property A. The fact that free groups and surface groups have Property A is due to Grossman and Schupp.
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