Results 281 to 290 of about 26,022 (315)

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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Algebra, Lie Group and Lie Algebra

2010
Geometry, algebra, and analysis are usually called the three main branches of mathematics. This chapter introduces some fundamental results in algebra that are mostly useful in systems and control. In section 4.1 some basic concepts of group and three homomorphism theorems are discussed. Ring and algebra are introduced briefly in section 4.2. As a tool,
Daizhan Cheng, Xiaoming Hu, Tielong Shen
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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 and Lie Algebra Representations

2017
In this chapter, we will introduce Lie algebras and Lie algebra representations, which provide a tractable linear construction that captures much of the behavior of Lie groups and Lie group representations.
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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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BUNDLES OF LIE ALGEBRAS

International Journal of Geometric Methods in Modern Physics, 2013
In this paper, a complete classification of completely irreducible closed linear bundles of Lie algebras is given. We also apply the so-called "Raïs formula" to compute the index of each of the Lie bundles of square matrices.
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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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Variational algorithms for linear algebra

Science Bulletin, 2021
Xiaosi Xu, Jinzhao Sun, Suguru Endo
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