Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
A bialgebra theory for Compatible Hom-Lie algebras
View through CrossRef
In this paper, we introduce the notions of matched pairs and Manin triple for compatible Hom-Lie algebras. Then, we give a bialgebra theory of compatible Hom-Lie algebras with emphasis on
its compatibility with Manin triple of compatible Hom-Lie algebras associated to a
nondegenerate symmetric bilinear form. Moreover, we study coboundary compatible Hom-Lie bialgebras. Finally, we investigate some properties of a representation of a Hom-Nijenhuis
Hom-Lie algebra and introduce the notion of a
Hom-Nijenhuis Hom-Lie coalgebra. Furthermore, a Hom-Nijenhuis
Hom-Lie bialgebra can be established by a Hom-Nijenhuis Hom-Lie algebra and a Hom-Nijenhuis Hom-Lie coalgebra satisfying some compatible
conditions.
Hacettepe University
Title: A bialgebra theory for Compatible Hom-Lie algebras
Description:
In this paper, we introduce the notions of matched pairs and Manin triple for compatible Hom-Lie algebras.
Then, we give a bialgebra theory of compatible Hom-Lie algebras with emphasis on
its compatibility with Manin triple of compatible Hom-Lie algebras associated to a
nondegenerate symmetric bilinear form.
Moreover, we study coboundary compatible Hom-Lie bialgebras.
Finally, we investigate some properties of a representation of a Hom-Nijenhuis
Hom-Lie algebra and introduce the notion of a
Hom-Nijenhuis Hom-Lie coalgebra.
Furthermore, a Hom-Nijenhuis
Hom-Lie bialgebra can be established by a Hom-Nijenhuis Hom-Lie algebra and a Hom-Nijenhuis Hom-Lie coalgebra satisfying some compatible
conditions.
Related Results
Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation
Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation
In this paper, we introduce the notion of a (regular) Hom-Lie group. We associate a Hom-Lie algebra to a Hom-Lie group and show that every regular Hom-Lie algebra is integrable. Th...
Construction of Hom-pre-Jordan algebras and Hom-J-dendriform algebras
Construction of Hom-pre-Jordan algebras and Hom-J-dendriform algebras
The aim of this work is to introduce and study the notions of Hom-pre-Jordan algebra and Hom-J-dendriform algebra which generalize Hom-Jordan algebras. Hom-pre-Jordan algebras are ...
3-Hom–Lie Yang–Baxter Equation and 3-Hom–Lie Bialgebras
3-Hom–Lie Yang–Baxter Equation and 3-Hom–Lie Bialgebras
In this paper, we first introduce the notion of a 3-Hom–Lie bialgebra and give an equivalent description of the 3-Hom–Lie bialgebras, the matched pairs and the Manin triples of 3-H...
Differential Antisymmetric Infinitesimal Bialgebras, Coherent Derivations and Poisson Bialgebras
Differential Antisymmetric Infinitesimal Bialgebras, Coherent Derivations and Poisson Bialgebras
We establish a bialgebra theory for differential algebras, called differential antisymmetric infinitesimal (ASI) bialgebras by generalizing the study of ASI bialgebras to the conte...
Symmetric Hom–Leibniz algebras
Symmetric Hom–Leibniz algebras
Abstract
This paper focuses on quadratic Hom–Leibniz algebras, defined as (left or right) Hom–Leibniz algebras equipped with symmetric, non-degenerate, and invariant bilinear fo...
Fuzzy Hom–Lie Ideals of Hom–Lie Algebras
Fuzzy Hom–Lie Ideals of Hom–Lie Algebras
In the given study, we intended to gain familiarity with the idea of fuzzy Hom–Lie subalgebras (ideals) of Hom–Lie algebras. It primarily seeks to study a few of their properties. ...
Hom-pre-Poisson superalgebras and Dual Hom-pre-Poisson superalgebras
Hom-pre-Poisson superalgebras and Dual Hom-pre-Poisson superalgebras
Abstract
In this research paper, we investigate the concept of Hom-superalgebras obtained by an internal law defined on ℤ2-graded vector space A equipped with an algebra mo...
Deformations and abelian extensions of compatible pre-Lie superalgebras
Deformations and abelian extensions of compatible pre-Lie superalgebras
In this paper, we give cohomologies and deformations theory, as well as abelian extensions for compatible pre-Lie superalgebras. Explicitly, we first introduce the notation of a co...