Related papers: Purely Hom-Lie bialgebras
We study a twisted version of the Yang-Baxter Equation, called the Hom-Yang-Baxter Equation (HYBE), which is motivated by Hom-Lie algebras. Three classes of solutions of the HYBE are constructed, one from Hom-Lie algebras and the others…
The purpose of this paper is to study the structure and the algebraic varieties of Hom-associative algebras. We give characterize multiplicative simple Hom-associative algebras and show some examples deforming the $2\times 2$-matrix algebra…
This paper is devoted to a classification of topological Lie bialgebra structures on the Lie algebra $\mathfrak{g}[\![x]\!]$, where $ \mathfrak{g} $ is a finite-dimensional simple Lie algebra over an algebraically closed field $ F $ of…
Lie admissible algebra structures, called center-symmetric algebras, are defined. Main properties and algebraic consequences are derived and discussed. Bimodules are given and used to build a center-symmetric algebra on the direct sum of…
From the definition and properties of unital hom-associative algebras, and the use of the Kaplansky's constructions, we develop new algebraic structures called 2-hom-associative bialgebras, 2-hom-bialgebras, and 2-2-hom-bialgebras. Besides,…
We propose a new approach to study coideal algebras. It is well-known that Manin triples (or equivalently Lie bi-algebra structures) are the requirement to deform Lie algebras and to obtain quantum groups. In this paper, introducing some…
In this work we give an inductive way to construct quadratic Hom-Lie algebras with twist maps in the centroid. We focus on those Hom-Lie algebras which are not Lie algebras. We prove that a Hom-Lie algebra of this type has trivial center…
We classify hom-Lie structures with nilpotent twisting map on $3$-dimensional complex Lie algebras, up to isomorphism, and classify all degenerations in such family. The ideas and techniques presented here can be easily extrapolated to…
In the category of Hom-Leibniz algebras we introduce the notion of representation as adequate coefficients to construct the chain complex to compute the Leibniz homology of Hom-Leibniz algebras. We study universal central extensions of…
In this paper, first we introduce the notion of quadratic Rota-Baxter Lie algebras of arbitrary weight, and show that there is a one-to-one correspondence between factorizable Lie bialgebras and quadratic Rota-Baxter Lie algebras of nonzero…
In the present paper, we aim to introduce the cohomology of $\mathcal{O}$-operators defined on the Hom-Lie conformal algebra concerning the given representation. To obtain the desired results, we describe three different cochain complexes…
We demonstrate how a simple linear-algebraic technique used earlier to compute low-degree cohomology of current Lie algebras, can be utilized to compute other kinds of structures on such Lie algebras, and discuss further generalizations,…
In this paper, we study the Manin triples associated to $n$-Lie bialgebras. We introduce the concept of operad matrices for $n$-Lie bialgebras. In particular, by studying a special case of operad matrices, it leads to the notion of local…
We study sympathetic Lie algebras, namely perfect and complete Lie algebras. They arise among other things in the study of adjoint Lie algebra cohomology. This is motivated by a conjecture of Pirashvili, which says that a non-trivial…
In this paper, we introduce the notions of Hom-tridendriform coalgebras and Hom-post-Lie coalgebras as the dual notions of Hom-tridendriform algebras and Hom-post-LIe algebras respectively. We give some properties related to them. Then, we…
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. Then, we define a Hom-exponential (Hexp) map from the Hom-Lie…
Motivated by recent work on Hom-Lie algebras and the Hom-Yang-Baxter equation, we introduce a twisted generalization of the classical Yang-Baxter equation (CYBE), called the classical Hom-Yang-Baxter equation (CHYBE). We show how an…
Hom-algebras are generalizations of algebras obtained using a twisting by a linear map. But there is a priori a freedom on where to twist. We enumerate here all the possible choices in the Lie and associative categories and study the…
In this article we will build a universal imbedding of a regular Hom- Lie triple system into a Lie algebra and show that the category of regular Hom-Lie triple systems is equivalent to a full subcategory of pairs of…
For any $n$-dimensional 3-Lie algebra $A$ over a field of characteristic zero with an involutive derivation $D$, we investigate the structure of the 3-Lie algebra $B_1=A\ltimes_{ad^*} A^* $ associated with the coadjoint representation…