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Universal Envelo** Algebras of Lie–Rinehart Algebras as a Left Adjoint Functor
We prove how the universal envelo** algebra constructions for Lie–Rinehart algebras and anchored Lie algebras are naturally left adjoint functors....
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A New Approach to Hom-Left-Symmetric Bialgebras
The main purpose of this paper is to consider a new definition of Hom-left-symmetric bialgebra. The coboundary Hom-left-symmetric bialgebra is also...
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Quantization of Color Lie Bialgebras
The main purpose of this paper is to study Quantization of color Lie bialgebras, generalizing to the color case the approach by Etingof–Kazhdan which...
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Epimorphic Quantum Subgroups and Coalgebra Codominions
We prove a number of results concerning monomorphisms, epimorphisms, dominions and codominions in categories of coalgebras. Examples include: (a)...
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2-Hom-Associative Bialgebras and Hom-Left Symmetric Dialgebras
From the definition and properties of unital hom-associative algebras, and the use of the Kaplansky’s construction, we develop algebraic structures...
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On a Class of Infinite Simple Lie Conformal Algebras
In this paper, we study a class of infinite simple Lie conformal algebras associated to a class of generalized Block type Lie algebras. The central...
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On Classification of (n+1)-Dimensional n-Hom-Lie Algebras with Nilpotent Twisting Maps
The aimKitouni, Abdennour Silvestrov, Sergei of this work is to study properties of n-Hom-Lie algebras in dimension...
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On Classification of (n \(+1\) )-Dimensional n-Hom-Lie Algebras for n \(=4,5,6\) and Nilpotent Twisting Map with 2-Dimensional Kernel
The aim of this work is to study properties of n-Hom-Lie algebras in dimension \(n+1\)...
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Cotwists of Bicomonads and BiHom-bialgebras
This paper presents the definition of the cotwists of a bicomonad, which offers a generalization of cotwists of bimonoids in duoidal categories. We...
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Hopf Algebras and Groups
In this chapter, we introduce bialgebras and Hopf algebras, as well as various fundamental related notions and constructions. We discuss briefly...
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Purely Hom-Lie bialgebras
In this paper, we first show that there is a Hom-Lie algebra structure on the set of ( σ , σ )-derivations of an associative algebra. Then we construct...
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Multiplicative n-Hom-Lie Color Algebras
Bakayoko, Ibrahima Silvestrov, SergeiThe purpose of this paper is to generalize some results on n-Lie algebras and n-Hom-Lie algebras to n-Hom-Lie...
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A Note on Graded Lie H-Pseudo-Bialgebras
We study the cohomology theory of graded Lie H -pseudoalgebras. Furthermore, using the differential of a 1-cochain in the reduced complex of graded...
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Parametric representations of BiHom-Hopf algebras
The main purpose of the present paper is to study representations of BiHom-Hopf algebras. We first introduce the notion of BiHom-Hopf algebras, and...
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Dual Lie Bialgebra Structures of W-algebra W(2, 2) Type
In the present paper, we investigate the dual Lie coalgebras of the centerless W (2, 2) algebra by studying the maximal good subspaces. Based on this,...
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On Hom-groups and Hom-group Actions
A Hom-group is the non-associative generalization of a group whose associativity and unitality are twisted by a compatible bijective map. In this...