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Invariant Lie Algebras and Lie Algebras with a Small Centroid
Algebra and Logic, 2001Let \(R\) 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
2017In 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, 1996The 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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On Derivations of Lie Algebras
Canadian Journal of Mathematics, 1976A 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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The Embedding of Lie Algebras in Restricted Lie Algebras
Journal of the London Mathematical Society, 1964openaire +1 more source
Conformal biderivations of loop W(a, b) Lie conformal algebra
Frontiers of Mathematics, 2021Lamei Yuan, Liangyun Chen
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A new kind of graded Lie algebra and parastatistical supersymmetry
Science in China Series A: Mathematics, 2001Sicong Jing
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A few expanding Lie algebras of the Lie algebra and applications
Physics Letters, Section A: General, Atomic and Solid State Physics, 2006Engui Fan
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