Results 81 to 90 of about 1,211 (118)
An algorithm for analysis of the structure of finitely presented Lie algebras
Discrete Mathematics & Theoretical Computer Science, 1997 We consider the following problem: what is the most general Lie algebra satisfying a given set of Lie polynomial equations? The presentation of Lie algebras by a finite set of generators and defining relations is one of the most general mathematical ...
Vladimir P. Gerdt, Vladimir V. Kornyak
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On algebraic Lie groups and algebr̀as [PDF]
Journal of the Mathematical Society of Japan, 1948 openaire +3 more sources
The Graded Lie Algebras of an Algebra
Indagationes Mathematicae (Proceedings), 1967 openaire +2 more sources
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On Contractions of Lie Algebras
Mathematics in Computer Science, 2016In this paper, the authors consider the notion of contraction of Lie algebras for the class of filiform Lie algebras, i.e. nilpotent Lie algebras with a maximal nilpotence index. This analysis is carried out using the notion of generalized derivations introduced in [\textit{P. Novotný} and \textit{J. Hrivnák}, J. Geom. Phys. 58, No.
J. M. Escobar +2 more
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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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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
2010Geometry, 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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Mathematics of the USSR-Sbornik, 1986
In this paper general problems of the deformations of Lie algebras over a field of characteristic zero and related problems of calculating the cohomologies with coefficients in the adjoint representation are considered. The author adapts and generalizes to the case of Lie algebras the general constructions of the cohomology theory of (local ...
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In this paper general problems of the deformations of Lie algebras over a field of characteristic zero and related problems of calculating the cohomologies with coefficients in the adjoint representation are considered. The author adapts and generalizes to the case of Lie algebras the general constructions of the cohomology theory of (local ...
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Affine Lie Algebra Modules and Complete Lie Algebras
Algebra Colloquium, 2006In 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, 1961LetLbe 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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