Results 1 to 10 of about 1,514 (129)
The Classical Hom–Leibniz Yang–Baxter Equation and Hom–Leibniz Bialgebras
Mathematics, 2022 In this paper, we first introduce the notion of Hom–Leibniz bialgebras, which is equivalent to matched pairs of Hom–Leibniz algebras and Manin triples of Hom–Leibniz algebras.
Shuangjian Guo +2 more
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O-operators and related structures on Leibniz algebras
Communications in Algebra, 2023 An $\mathcal{O}$-operator has been used to extend a Leibniz algebra by its representation. In this paper, we investigate several structures related to $\mathcal{O}$-operators on Leibniz algebras and introduce (dual) $\mathcal{O}$N-structures on Leibniz algebras associated to their representations.
Naihuan Jing, Sun Qinxiu
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Journal of Nonlinear Mathematical PhysicsAbstract In this paper, first we introduce the notions of 3-pre-Leibniz algebras and relative Rota-Baxter operators on 3-Leibniz algebras. We show that a 3-pre-Leibniz algebra gives rise to a 3-Leibniz algebra and a representation such that the identity map is a relative Rota-Baxter operator.
Yanqiu Zhou, Song Lina, Hou Shuai
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Quasi-triangular, factorizable Leibniz bialgebras and relative Rota–Baxter operators
Forum MathematicumAbstract We introduce the notion of quasi-triangular Leibniz bialgebras, which can be constructed from solutions of the classical Leibniz Yang–Baxter equation (CLYBE) whose skew-symmetric parts are invariant. In addition to triangular Leibniz bialgebras, quasi-triangular Leibniz bialgebras contain factorizable Leibniz bialgebras as ...
Rong Tang, Yunhe Sheng, Chengming Bai
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Leibniz bialgebras, relative Rota–Baxter operators, and the classical Leibniz Yang–Baxter equation [PDF]
Journal of Noncommutative Geometry, 2022 In this paper, first we introduce the notion of a Leibniz bialgebra and show that matched pairs of Leibniz algebras, Manin triples of Leibniz algebras, and Leibniz bialgebras are equivalent. Then we introduce the notion of a (relative) Rota–Baxter operator on a Leibniz algebra and construct the graded Lie algebra that characterizes
Rong Tang, Yunhe Sheng
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On theoretical and practical aspects of Duhamel’s integral [PDF]
Archives of Control Sciences, 2021 The paper is a newapproach to the Duhamel integral. It contains an overviewof formulas and applications of Duhamel’s integral as well as a number of new results on the Duhamel integral and principle.
Michał Różański +3 more
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The Generalized Discrete Proportional Derivative and Its Applications
Fractal and Fractional, 2023 The aim of this paper is to define the generalized discrete proportional derivative (GDPD) and illustrate the application of the Leibniz theorem, the binomial expansion, and Montmort’s formulas in the context of the generalized discrete proportional case.
Rajiniganth Pandurangan +3 more
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On the gauge-natural operators similar to the twisted Dorfman-Courant bracket [PDF]
Opuscula Mathematica, 2021 All \(\mathcal{VB}_{m,n}\)-gauge-natural operators \(C\) sending linear \(3\)-forms \(H \in \Gamma^{l}_E(\bigwedge^3T^*E)\) on a smooth (\(\mathcal{C}^\infty\)) vector bundle \(E\) into \(\mathbf{R}\)-bilinear operators \[C_H:\Gamma^l_E(TE \oplus T^*E ...
Włodzimierz M. Mikulski
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Deformations of relative Rota–Baxter operators on Leibniz algebras [PDF]
International Journal of Geometric Methods in Modern Physics, 2020 In this paper, we introduce the cohomology theory of relative Rota–Baxter operators on Leibniz algebras. We use the cohomological approach to study linear and formal deformations of relative Rota–Baxter operators. In particular, the notion of Nijenhuis elements is introduced to characterize trivial linear deformations.
Rong Tang, Yunhe Sheng, Yanqiu Zhou
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Reynolds operators on Hom-Leibniz algebras
Filomat, 2023 In this paper, we first introduce the notion of Reynolds operators on Hom-Leibniz algebras and give some constructions. Furthermore, we define the cohomology of Reynolds operators, and use this cohomology to study deformations of Reynolds operators.
Dingguo Wanga, Yuanyuan Keb
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