Derivations of the algebra . (Dérivations de l'algèbre .)
Ben Yakoub, L., Louly, A. (2009)
Beiträge zur Algebra und Geometrie
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Ben Yakoub, L., Louly, A. (2009)
Beiträge zur Algebra und Geometrie
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Ciobanu, Camelia (2007)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Jia Zhou, Liangyun Chen, Yao Ma (2016)
Open Mathematics
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In this paper, we present some basic properties concerning the derivation algebra Der (T), the quasiderivation algebra QDer (T) and the generalized derivation algebra GDer (T) of a Lie triple system T, with the relationship Der (T) ⊆ QDer (T) ⊆ GDer (T) ⊆ End (T). Furthermore, we completely determine those Lie triple systems T with condition QDer (T) = End (T). We also show that the quasiderivations of T can be embedded as derivations in a larger Lie triple system.
Ivan Kaygorodov, Yury Popov (2016)
Open Mathematics
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Yanbo Li, Feng Wei (2015)
Colloquium Mathematicae
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Let K be a field and Γ a finite quiver without oriented cycles. Let Λ := K(Γ,ρ) be the quotient algebra of the path algebra KΓ by the ideal generated by ρ, and let 𝒟(Λ) be the dual extension of Λ. We prove that each Lie derivation of 𝒟(Λ) is of the standard form.
J. de Ruiter (1974)
Compositio Mathematica
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Chunyue Wang, Qingcheng Zhang (2018)
Czechoslovak Mathematical Journal
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We construct a 3-Lie 2-algebra from a 3-Leibniz algebra and a Rota-Baxter 3-Lie algebra. Moreover, we give some examples of 3-Leibniz algebras.
Kenny De Commer (2015)
Banach Center Publications
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On the level of Lie algebras, the contraction procedure is a method to create a new Lie algebra from a given Lie algebra by rescaling generators and letting the scaling parameter tend to zero. One of the most well-known examples is the contraction from 𝔰𝔲(2) to 𝔢(2), the Lie algebra of upper-triangular matrices with zero trace and purely imaginary diagonal. In this paper, we will consider an extension of this contraction by taking also into consideration the natural bialgebra structures...
de Graaf, W.A. (2005)
Experimental Mathematics
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Cohen, A.M., de Graaf, W.A., Rónyai, L. (1997)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Dev Karan Singh, Mani Shankar Pandey, Shiv Datt Kumar (2024)
Czechoslovak Mathematical Journal
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This paper aims to introduce and explore the concept of Lie perfect multiplicative Lie algebras, with a particular focus on their connections to the central extension theory of multiplicative Lie algebras. The primary objective is to establish and provide proof for a range of results derived from Lie perfect multiplicative Lie algebras. Furthermore, the study extends the notion of Lie nilpotency by introducing and examining the concept of local nilpotency within multiplicative Lie algebras....
Galitski, L.Yu., Timashev, D.A. (1999)
Journal of Lie Theory
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Richter, David A. (1999)
Journal of Lie Theory
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Bing Sun, Liangyun Chen (2015)
Open Mathematics
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In this paper, we introduce the definition of restrictable Lie-Rinehart algebras, the concept of restrictability is by far more tractable than that of a restricted Lie-Rinehart algebra. Moreover, we obtain some properties of p-mappings and restrictable Lie-Rinehart algebras. Finally, we give some sufficient conditions for the commutativity of quasi-toral restricted Lie-Rinehart algebras and study how a quasi-toral restricted Lie-Rinehart algebra with zero center and of minimal dimension...