Results 11 to 20 of about 39,911 (195)
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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Where Mathematical Symbols Come From. [PDF]
Top Cogn SciAbstract There is a sense in which the symbols used in mathematical expressions and formulas are arbitrary. After all, arithmetic would be no different if we would replace the symbols ‘+$+$’ or ‘8’ by different symbols. Nevertheless, the shape of many mathematical symbols is in fact well motivated in practice.
Schlimm D.
europepmc +2 more sources
Complete Leibniz Algebras [PDF]
Journal of Algebra, 2020 Leibniz algebras are certain generalization of Lie algebras. It is natural to generalize concepts in Lie algebras to Leibniz algebras and investigate whether the corresponding results still hold. In this paper we introduce the notion of complete Leibniz algebras as generalization of complete Lie algebras.
Boyle, Kristen +2 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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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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Solvable Leibniz Algebras with Filiform Nilradical [PDF]
, 2015 In this paper we continue the description of solvable Leibniz algebras whose nilradical is a filiform algebra. In fact, solvable Leibniz algebras whose nilradical is a naturally graded filiform Leibniz algebra are described in [6] and [8].
Camacho Santana, Luisa María +2 more
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MINIMAL NONNILPOTENT LEIBNIZ ALGEBRAS
International Electronic Journal of Algebra, 2020 We classify all nonnilpotent, solvable Leibniz algebras with the property that all proper subalgebras are nilpotent. This generalizes the work of Stitzinger and Towers in Lie algebras. We show several examples which illustrate the differences between the Lie and Leibniz results.
BOSKO-DUNBAR, Lindsey +3 more
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The local integration of Leibniz algebras [PDF]
, 2012 This article gives a local answer to the coquecigrue problem. Hereby we mean the problem, formulated by J-L. Loday in \cite{LodayEns}, is that of finding a generalization of the Lie's third theorem for Leibniz algebra.
Covez, Simon
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E6(6) exceptional Drinfel’d algebras
Journal of High Energy Physics, 2021 The exceptional Drinfel’d algebra (EDA) is a Leibniz algebra introduced to provide an algebraic underpinning with which to explore generalised notions of U-duality in M-theory. In essence, it provides an M-theoretic analogue of the way a Drinfel’d double
Emanuel Malek +2 more
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