Results 11 to 20 of about 456,826 (227)
On Inner Derivations of Leibniz Algebras
MathematicsLeibniz algebras are generalizations of Lie algebras. Similar to Lie algebras, inner derivations play a crucial role in characterizing complete Leibniz algebras.
Sutida Patlertsin +2 more
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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 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 structure of the algebra of derivations of cyclic Leibniz algebras [PDF]
, 2021 We describe the algebra of derivation of finitedimensional cyclic Leibniz ...
Yashchuk, V.S. +2 more
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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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Two-step nilpotent Leibniz algebras [PDF]
, 2022 In this paper we give a complete classification of two-step nilpotent Leibniz algebras in terms of Kronecker modules associated with pairs of bilinear forms.
Mancini, Manuel +3 more
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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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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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Leibniz algebras with absolute maximal lie subalgebras [PDF]
, 2020 A Lie subalgebra of a given Leibniz algebra is said to be an absolute maximal Lie subalgebra if it has codimension one. In this paper, we study some properties of non-Lie Leibniz algebras containing absolute maximal Lie subalgebras.
Tcheka, C. +3 more
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From Groups to Leibniz Algebras: Common Approaches, Parallel Results [PDF]
Advances in Group Theory and Applications, 2018 In this article, we study (locally) nilpotent and hyper-central Leibniz algebras. We obtained results similar to those in group theory. For instance, we proved a result analogous to the Hirsch-Plotkin Theorem for locally nilpotent groups.
L.A. Kurdachenko +2 more
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