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.
Amir Hosein Mokhtari, Fahimeh Moafian, Hamid Reza Ebrahimi Vishki (2017)
Annales Mathematicae Silesianae
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In this paper we provide some conditions under which a Lie derivation on a trivial extension algebra is proper, that is, it can be expressed as a sum of a derivation and a center valued map vanishing at commutators. We then apply our results for triangular algebras. Some illuminating examples are also included.
Galitski, L.Yu., Timashev, D.A. (1999)
Journal of Lie Theory
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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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Ben Yakoub, L., Louly, A. (2009)
Beiträge zur Algebra und Geometrie
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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...
de Graaf, W.A. (2005)
Experimental Mathematics
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M. Cabrera, J. Martínez Moreno, A. Rodríguez (1986)
Extracta Mathematicae
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Paolo Casati (2011)
Banach Center Publications
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In this paper we construct on truncated current Lie algebras integrable hierarchies of partial differential equations, which generalize the Drinfeld-Sokolov hierarchies defined on Kac-Moody Lie algebras.
Crandall, Gordon, Dodziuk, Jósef (2002)
Journal of Lie Theory
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Richter, David A. (1999)
Journal of Lie Theory
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Doubrov, Boris M., Komrakov, Boris P. (1999)
Geometry & Topology
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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...
J. de Ruiter (1974)
Compositio Mathematica
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Alberto C. Elduque Palomo (1986)
Extracta Mathematicae
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In this paper the structure of the maximal elements of the lattice of subalgebras of central simple non-Lie Malcev algebras is considered. Such maximal subalgebras are studied in two ways: first by using theoretical results concerning Malcev algebras, and second by using the close connection between these simple non-Lie Malcev algebras and the Cayley-Dickson algebras, which have been extensively studied (see [4]).