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Search: MSC category 17B05 ( Structure theory )

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1. CMB Online first

Leandro, Cagliero; Szechtman, Fernando
 Jordan-Chevalley decomposition in Lie algebras We prove that if $\mathfrak{s}$ is a solvable Lie algebra of matrices over a field of characteristic 0, and $A\in\mathfrak{s}$, then the semisimple and nilpotent summands of the Jordan-Chevalley decomposition of $A$ belong to $\mathfrak{s}$ if and only if there exist $S,N\in\mathfrak{s}$, $S$ is semisimple, $N$ is nilpotent (not necessarily $[S,N]=0$) such that $A=S+N$. Keywords:solvable Lie algebra, Jordan-Chevalley decomposition, representationCategories:17-08, 17B05, 20C40, 15A21

2. CMB 2008 (vol 51 pp. 298)

Tocón, Maribel
 The Kostrikin Radical and the Invariance of the Core of Reduced Extended Affine Lie Algebras In this paper we prove that the Kostrikin radical of an extended affine Lie algebra of reduced type coincides with the center of its core, and use this characterization to get a type-free description of the core of such algebras. As a consequence we get that the core of an extended affine Lie algebra of reduced type is invariant under the automorphisms of the algebra. Keywords:extended affine Lie algebra, Lie torus, core, Kostrikin radicalCategories:17B05, 17B65

3. CMB 2002 (vol 45 pp. 525)

Berman, Stephen; Morita, Jun; Yoshii, Yoji
 Some Factorizations in Universal Enveloping Algebras of Three Dimensional Lie Algebras and Generalizations We introduce the notion of Lie algebras with plus-minus pairs as well as regular plus-minus pairs. These notions deal with certain factorizations in universal enveloping algebras. We show that many important Lie algebras have such pairs and we classify, and give a full treatment of, the three dimensional Lie algebras with plus-minus pairs. Categories:17B05, 17B35, 17B67, 17B70
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