Results 11 to 20 of about 156 (136)
Subinvariance in Leibniz algebras [PDF]
Journal of Algebra, 2021 Leibniz algebras are certain generalizations of Lie algebras. Motivated by the concept of subinvariance in group theory, Schenkman studied properties of subinvariant subalgebras of a Lie algebra. In this paper we define subinvariant subalgebras of Leibniz algebras and study their properties.
Kailash C. Misra +2 more
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On the derivations of cyclic Leibniz algebras
Karpatsʹkì Matematičnì Publìkacìï, 2022 Let $L$ be an algebra over a field $F$. Then $L$ is called a left Leibniz algebra, if its multiplication operation $[-,-]$ additionally satisfies the so-called left Leibniz identity: $[[a,b],c]=[a,[b,c]]-[b,[a,c]]$ for all elements $a,b,c\in L$. A linear
M.M. Semko, L.V. Skaskiv, O.A. Yarovaya
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On metric Leibniz algebras and deformations [PDF]
International Journal of Algebra and Computation, 2022 In this note, we consider low-dimensional metric Leibniz algebras with an invariant inner product over the complex numbers up to dimension 5. We study their deformations, and give explicit formulas for the cocycles and deformations. We identify among those the metric deformations.
Alice Fialowski, Ashis Mandal
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On the derivations of Leibniz algebras of low dimension
Доповiдi Нацiональної академiї наук України, 2023 Let L be an algebra over a field F. Then L is called a left Leibniz algebra if its multiplication operations [×, ×] addition- ally satisfy the so-called left Leibniz identity: [[a,b],c] = [a,[b,c]] – [b,[a,c]] for all elements a, b, c Î L. In this paper,
L.A. Kurdachenko +2 more
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Description of the automorphism groups of some Leibniz algebras
Researches in Mathematics, 2023 Let $L$ be an algebra over a field $F$ with the binary operations $+$ and $[,]$. Then $L$ is called a left Leibniz algebra if it satisfies the left Leibniz identity: $[[a,b],c]=[a,[b,c]]-[b,[a,c]]$ for all elements $a,b,c\in L$.
L.A. Kurdachenko, O.O. Pypka, M.M. Semko
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Leibniz Algebras and Lie Algebras [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2013 This paper concerns the algebraic structure of finite-dimensional complex Leibniz algebras. In particular, we introduce left central and symmetric Leibniz algebras, and study the poset of Lie subalgebras using an associative bilinear pairing taking values in the Leibniz kernel.
Mason, G., Yamskulna, G.
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On ideals and contraideals in Leibniz algebras
Доповiдi Нацiональної академiї наук України, 2023 A subalgebra S of a Leibniz algebra L is called a contraideal, if an ideal, generated by S coincides with L. We study the Leibniz algebras, whose subalgebras are either an ideal or a contraideal.
L.A. Kurdachenko +2 more
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Representations of Leibniz Algebras [PDF]
Algebras and Representation Theory, 2014 This paper is devoted to the study of irreducible representations of Leibniz algebras. The authors establish a result which claims that irreducible Leibniz representations are very closely related to irreducible representations of the corresponding Lie algebra.
Fialowski, A., Mihálka, É. Zs.
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Communications in Mathematics, 2020 Abstract A finite-dimensional Lie algebra is called an A-algebra if all of its nilpotent subalgebras are abelian. These arise in the study of constant Yang-Mills potentials and have also been particularly important in relation to the problem of describing residually finite varieties.
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On the algebra of derivations of some nilpotent Leibniz algebras
Researches in Mathematics, 2023 We describe the algebra of derivations of some nilpotent Leibniz algebra, having dimensionality 3.
L.A. Kurdachenko +2 more
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