Results 231 to 240 of about 2,410,088 (276)

SANDWICHES IN LIE ALGEBRAS

Mathematics of the USSR-Sbornik, 1981
The author investigates Lie algebras which contain elements the squares of whose adjoint endomorphisms are zero. The basic theory is used, in particular, to improve the proof of the local nilpotence of Engel Lie algebras. Bibliography: 3 titles.
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Affine Lie Algebra Modules and Complete Lie Algebras

Algebra Colloquium, 2006
In this paper, we first construct some new infinite dimensional Lie algebras by using the integrable modules of affine Lie algebras. Then we prove that these new Lie algebras are complete. We also prove that the generalized Borel subalgebras and the generalized parabolic subalgebras of these Lie algebras are complete.
Gao, Yongcun, Meng, Daoji
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On the Derivation Algebras of Lie Algebras

Canadian Journal of Mathematics, 1961
LetLbe a Lie algebra over a field of characteristic 0 and letD(L)be the derivation algebra ofL, that is, the Lie algebra of all derivations ofL. Then it is natural to ask the following questions: What is the structure ofD(L)?What are the relations of the structures ofD(L)andL?
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Invariant Lie Algebras and Lie Algebras with a Small Centroid

Algebra and Logic, 2001
Let \(R\) be an algebra, \(\Gamma(R)\) be its centroid and \(A(R):=\{\phi\in\Gamma(R):\phi R\subseteq \text{Ann}(R)\}\). \(\Gamma(R)\) is called small if, for some decomposition of \(R\) into a finite direct sum of directly indecomposable algebras \(R_i\), the factors \(\Gamma(R_i)/A(R_i)\) are fields. Generalizing the result of \textit{D. J. Melville}
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Lie Algebras

Algebra 4, 2021
R. Lal
semanticscholar   +1 more source

Finite Presentations of Lie Algebras And Restricted Lie Algebras

Bulletin of the London Mathematical Society, 1996
The author proves a version of the Golod-Shafarevich theorem for a large class of Lie algebras, including all finite-dimensional and all soluble Lie algebras. Specifically, suppose that \(L\) is a finite-dimensional or soluble Lie algebra over a field \(k\) which has a presentation with \(n\) generators and \(r\) relations.
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Introduction to Lie Algebras and Representation Theory

, 1973
J. Humphreys
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Infinite-dimensional Lie algebras

, 1974
R. Amayo, I. Stewart
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On Derivations of Lie Algebras

Canadian Journal of Mathematics, 1976
A well known result in the theory of Lie algebras, due to H. Zassenhaus, states that if is a finite dimensional Lie algebra over the field K such that the killing form of is non-degenerate, then the derivations of are all inner, [3, p. 74]. In particular, this applies to the finite dimensional split simple Lie algebras over fields of characteristic ...
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Lie Groups, Lie Algebras, and Representations

, 2003
B. Hall
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