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Mathematical Notes, 2006
A Leibniz algebra \(L\) is said to be \textit{thin} if \(\dim(L^1/L^2)=2\) and \(\dim(L_i/L_{i+1})=1\) for all \(i\geq 2\). Here \(L^1=L\) and \(L^{n+1}=[L^n,L]\). The author proves that there are three classes of non-Lie thin Leibniz algebras.
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A Leibniz algebra \(L\) is said to be \textit{thin} if \(\dim(L^1/L^2)=2\) and \(\dim(L_i/L_{i+1})=1\) for all \(i\geq 2\). Here \(L^1=L\) and \(L^{n+1}=[L^n,L]\). The author proves that there are three classes of non-Lie thin Leibniz algebras.
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ON NILPOTENT LEIBNIZ n-ALGEBRAS
Journal of Algebra and Its Applications, 2012We study the nilpotency of Leibniz n-algebras related with the adapted version of Engel's theorem to Leibniz n-algebras. We also deal with the characterization of finite-dimensional nilpotent complex Leibniz n-algebras.
Camacho, L. M. +4 more
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2004
Leibniz algebras are possible non-(anti)commutative analogs of Lie algebras. These algebras have appeared in [55] under the name “D-algebras”. In [221, 222, 223] J.-L. Loday and T. Pirashvili studied these analogs from the point of view of homological algebra.
Alexander A. Mikhalev +2 more
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Leibniz algebras are possible non-(anti)commutative analogs of Lie algebras. These algebras have appeared in [55] under the name “D-algebras”. In [221, 222, 223] J.-L. Loday and T. Pirashvili studied these analogs from the point of view of homological algebra.
Alexander A. Mikhalev +2 more
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2014
Left (or right) Leibniz algebras endowed with symmetric non-degenerate and associative bilinear forms (called quadratic Leibniz algebras) are investigated. In particular, we prove that left (resp. right) Leibniz algebras that carry this structure are also right (resp. left) Leibniz algebras.
Benayadi, Saïd, Hidri, Samiha
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Left (or right) Leibniz algebras endowed with symmetric non-degenerate and associative bilinear forms (called quadratic Leibniz algebras) are investigated. In particular, we prove that left (resp. right) Leibniz algebras that carry this structure are also right (resp. left) Leibniz algebras.
Benayadi, Saïd, Hidri, Samiha
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Leibniz and Lie Algebra Structures for Nambu Algebra
Letters in Mathematical Physics, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Daletskii, Yuri L., Takhtajan, Leon A.
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On the Automorphism Groups for Some Leibniz Algebras of Low Dimensions
Ukrainian Mathematical Journal, 2023L. A. Kurdachenko, O. Pypka, T. Velychko
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Abelian Subalgebras and Ideals of Maximal Dimension in Solvable Leibniz Algebras
Mediterranean Journal of Mathematics, 2023M. Ceballos, D. Towers
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ON REPRESENTATIONS OF SYMMETRIC LEIBNIZ ALGEBRAS
Glasgow Mathematical Journal, 2019AbstractWe give a new and useful approach to study the representations of symmetric Leibniz algebras. Using this approach, we obtain some results on the representations of these algebras.
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Crossed Modules and Non-Abelian Extensions of Rota-Baxter Leibniz Algebras
Social Science Research Network, 2023B. Hou, Yanhong Guo
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