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3-pre-Leibniz Algebras, Deformations and Cohomologies of Relative Rota-Baxter Operators on 3-Leibniz Algebras
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...
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Hom-Leibniz bialgebras and BiHom-Leibniz dendriform algebras
A notion of a Hom-Leibniz bialgebra is introduced and it is shown that matched pairs of Hom-Leibniz algebras, Manin triples of Hom-Leibniz algebras...
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Cohomology of Leibniz Algebras
This is a survey on new developments in the cohomology of Leibniz algebras for the Deutsche Mathematiker Vereinigung. We will mainly report on...
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Classification of Five-Dimensional Symmetric Leibniz Algebras
In this paper, we give the complete classification of 5-dimensional complex solvable symmetric Leibniz algebras.
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Local Derivations and Automorphisms of Direct Sum Null-Filiform Leibniz Algebras
AbstractThis paper is devoted to study local derivations and automorphism of some nilpotent Leibniz algebras. We prove that direct sum null-filiform...
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Abelian Subalgebras and Ideals of Maximal Dimension in Solvable Leibniz Algebras
In this paper, we compare the abelian subalgebras and ideals of maximal dimension for finite-dimensional Leibniz algebras. We study Leibniz algebras...
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Erratum: Weighted Fractional Leibniz-type Rules for Bilinear Multiplier Operators
Erratum to article [
1 ]: J. Brummer and V. Naibo, Weighted fractional Leibniz-type rules for bilinear multiplier operators, Potential Anal. 51 (1),... -
Local Superderivations on Solvable Lie and Leibniz Superalgebras
Throughout this paper, we show on one hand, that there are nilpotent and solvable Lie superalgebras with infinitely many local superderivations which...
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Leibniz on Number Systems
This chapter examines the pioneering work of Gottfried Wilhelm Leibniz (1646–1716) on various number systems, in particular binary, which he...
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Fractional Leibniz-type Rules on Spaces of Homogeneous Type
Let ( M , ρ , μ ) be a space of homogeneous type satisfying the reverse doubling condition and the non-collapsing condition. In view of the lack of the...
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Leibniz Algebras, Some Basic Concepts
This chapter introduces the concepts of Leibniz algebras, delineates their initial basic properties, considers their basic subalgebras and some...
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Fractional Leibniz Rules in the Setting of Quasi-Banach Function Spaces
Fractional Leibniz rules are reminiscent of the product rule learned in calculus classes, offering estimates in the Lebesgue norm for fractional...
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Ternary Leibniz Color Algebras and Beyond
The purpose of this paper is to study some ternary color algebras. We generalize some results on ternary Leibniz algebras to the case of ternary...
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Leibniz-Type Rules for Bilinear Fourier Multiplier Operators with Besov Regularity
We establish the Leibniz-type rules for bilinear Fourier multiplier operators with Besov regularity in Lebesgue spaces and mixed Lebesgue spaces.
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Leibniz algebras with derivations
In this paper, we consider Leibniz algebras with derivations. A pair consisting of a Leibniz algebra and a distinguished derivation is called a...
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Leibniz on Number Systems
This chapter examines the pioneering work of Gottfried Wilhelm Leibniz (1646–1716) on various number systems, in particular binary, which he...
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Varieties of Null-Filiform Leibniz Algebras Under the Action of Hopf Algebras
Let L be an n -dimensional null-filiform Leibniz algebra over a field K . We consider a finite dimensional cocommutative Hopf algebra or a Taft algebra H ...
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Weighted Leibniz-type rules for bilinear flag multipliers
We establish Leibniz type rules for bilinear flag multipliers with limited regularity in the Lebesgue spaces with flag weights. As applications, we...