Results 41 to 50 of about 156 (136)
On the structure of Leibniz algebras, whose subalgebras are ideals or core-free
Доповiдi Нацiональної академiї наук УкраїниAn algebra L over a field F is said to be a Leibniz algebra (more precisely, a left Leibniz algebra), if it satisfies the Leibniz identity: [[a, b], c] = [a, [b, c]] — [b, [a, c]] for all a, b, c ∈ L. Leibniz algebras are generalizations of Lie algebras.
V.A. Chupordia +2 more
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Exploring exceptional Drinfeld geometries
Journal of High Energy Physics, 2020 We explore geometries that give rise to a novel algebraic structure, the Exceptional Drinfeld Algebra, which has recently been proposed as an approach to study generalised U-dualities, similar to the non-Abelian and Poisson-Lie generalisations of T ...
Chris D. A. Blair +2 more
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On Integral Manifolds for Leibniz Algebras [PDF]
Algebra, 2014 We discuss several partial solutions to the so-called “coquecigrue problem” of Loday; these solutions parallel, but also generalize in several directions, the classical Lie group-Lie algebra correspondence. Our study highlights some clear similarities between the split and nonsplit cases and leads us to a general unifying scheme that provides an answer
Juan Monterde, Fausto Ongay
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Leibniz’s Binary Algebra and its Role in the Expression and Classification of Numbers
Philosophia Scientiæ, 2021 Leibniz’s binary numeral system is generally studied for its arithmetical relevance, but the analysis of several unpublished manuscripts shows that from the very beginning Leibniz also envisaged a new form of algebra in the context of dyadics based on ...
Mattia Brancato
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A Characterization of Nilpotent Leibniz Algebras [PDF]
Algebras and Representation Theory, 2012 arXiv admin note: text overlap with arXiv:1103 ...
Fialowski, Alice +2 more
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A new model of the free monogenic digroup
Математичні Студії, 2023 It is well-known that one of open problems in the theory of Leibniz algebras is to find a suitable generalization of Lie’s third theorem which associates a (local) Lie group to any Lie algebra, real or complex. It turns out, this is related to finding an
Yu. V. Zhuchok, G. F. Pilz
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Feedback Linearisation with State Constraints
International Journal of Robust and Nonlinear Control, EarlyView.ABSTRACT Feedback Linearisation (FBL) is a widely used technique that applies feedback laws to transform input‐affine nonlinear control systems into linear control systems, allowing for the use of linear controller design methods such as pole placement.
Songlin Jin, Yuanbo Nie, Morgan Jones
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Automorphism groups of some non-nilpotent Leibniz algebras
Researches in MathematicsLet $L$ 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 $a,b,c\in L$. A linear transformation $f$ of $L$
L.A. Kurdachenko +2 more
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The Additive Logic of Epistemic Reasons: An Axiomatic Account
Theoria, EarlyView.ABSTRACT The article argues for a system of axioms that is meant to capture the logic of normative reasons for belief. The system concerns a primitive direct‐reason relation, a defined doxastic‐reason relation, and a primitive function for the revision of rational belief by reasons.
Hannes Leitgeb
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SciPost Physics, 2021 We propose a Leibniz algebra, to be called DD$^+$, which is a generalization of the Drinfel'd double. We find that there is a one-to-one correspondence between a DD$^+$ and a Jacobi--Lie bialgebra, extending the known correspondence between a Lie ...
Jose J. Fernandez-Melgarejo, Yuho Sakatani
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