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Structured Dynamics in the Algorithmic Agent. [PDF]

open access: yesEntropy (Basel)
Ruffini G, Castaldo F, Vohryzek J.
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Binary Leibniz Algebras

Mathematical Notes, 2021
For a class of algebras \(\mathcal{A}\), denote by \(\mathcal{A}_1\) the class of algebras in which every singly generated algebra belongs to the class \(\mathcal{A}\). We similarly define \(\mathcal{A}_2\) as the class of algebras in which every two-generated algebra belongs to the class \(\mathcal{A}\).
Ismailov, N. A., Dzhumadil'daev, A. S.
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On complete Leibniz algebras

International Journal of Algebra and Computation, 2022
This paper is devoted to the so-called complete Leibniz algebras. We construct some complete Leibniz algebras with complete radical and prove that the direct sum of complete Leibniz algebras is also complete. It is known that a Lie algebra with a complete ideal is split.
Shavkat A. Ayupov   +2 more
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On the commutator in Leibniz algebras

International Journal of Algebra and Computation, 2022
We prove that the class of algebras embeddable into Leibniz algebras with respect to the commutator product is not a variety. It is shown that every commutative metabelain algebra is embeddable into Leibniz algebras with respect to the anti-commutator. Furthermore, we study polynomial identities satisfied by the commutator in every Leibniz algebra. We
A. S. Dzhumadil'daev   +2 more
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Cohomology of Leibniz Algebras

Jahresbericht der Deutschen Mathematiker-Vereinigung, 2023
The paper under review is a survey of recent results on the cohomology of Leibniz algebras which are due to the author and the reviewer [J. Algebra 569, 276--317 (2021; Zbl 1465.17006); Indag. Math., New Ser. 35, No. 1, 87--113 (2024; Zbl 1543.17003)].
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