Results 11 to 20 of about 455 (185)
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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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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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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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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Қарағанды университетінің хабаршысы. Математика сериясы, 2023 In recent years there has been a great interest in the study of Zinbiel (dual Leibniz) algebras. Let A be Zinbiel algebra over an arbitrary field K and let e1,e2,...,em,... be a linear basis of A. In 2010 A.
D.M. Zhangazinova, A.S. Naurazbekova
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On Restricted Leibniz Algebras
Communications in Algebra, 2006 In this paper we prove that in prime characteristic there is a functor $-_{p-Leib}$ from the category of diassociative algebras to the category of restricted Leibniz algebras, generalizing the functor from associative algebras to restricted Lie algebras.
Dokas, Ioannis, Loday, Jean-Louis
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On a class of Leibniz algebras
International Journal of Advanced Mathematical Sciences, 2015 <p>We pointed out the class of Leibniz algebras such that the Killing form is non degenerate implies algebras are semisimple.</p>
Béré, Côme J. A. +2 more
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Conjugacy of Cartan Subalgebras in Solvable Leibniz Algebras and Real Leibniz Algebras [PDF]
Algebras and Representation Theory, 2017 This paper is devoted to study the conjugacy of Cartan subalgebras in solvable Leibniz algebras. A Leibniz algebra is nonantisymmetric generalization of Lie algebras. Since proofs of conjugacy results in Lie algebras depend on antisymmetry property, the authors prove the analogues of conjugacy results by amending the arguments in Leibniz algebras.
Stitzinger, Ernie, White, Ashley
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