# Hom-Lie structures on Kac–Moody algebras

```@article{Makhlouf2018HomLieSO,
title={Hom-Lie structures on Kac–Moody algebras},
author={Abdenacer Makhlouf and Pasha Zusmanovich},
journal={Journal of Algebra},
year={2018}
}```
• Published 1 May 2018
• Mathematics
• Journal of Algebra
14 Citations
When Hom-Lie structures form a Jordan algebra
A BSTRACT . We are concerned with the question when Hom-Lie structures on a Lie algebra are closed with respect to the Jordan product. Somewhat unexpectedly, this leads us to certain questions
Hom-Lie structures on 3-dimensional skew symmetric algebras
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• 2019
We describe the dimension of the space of possible linear endomorphisms that turn skew-symmetric three-dimensional algebras into Hom-Lie algebras. We find a correspondence between the rank of a mat
Classification of Low-Dimensional Hom-Lie Algebras
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• 2020
We derive conditions for an arbitrary n-dimensional algebra to be a Hom-Lie algebra, in the form of a system of polynomial equations, containing both structure constants of the skew-symmetric bilin
Ado theorem for nilpotent Hom-Lie algebras
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Int. J. Algebra Comput.
• 2019
We prove an analog of the Ado theorem — the existence of a finite-dimensional faithful representation — for a certain kind of finite-dimensional nilpotent Hom–Lie algebras.
Equivariant one-parameter formal deformations of Hom-Leibniz algebras
• Mathematics
• 2019
We introduce an equivariant \$1\$-parameter formal deformation theory of Hom-Leibniz algebras equipped with finite group actions on Hom-Leibniz algebras. We define a suitable equivariant deformation
Equivariant formal deformations of Hom-pre-Lie algebras
• Mathematics
• 2021
In this paper, we define a new cohomology theory for multiplicative Hom-preLie algebras which controls deformations of Hom-pre-Lie algebra structure. This new cohomology is a natural one considering
Regular Hom-Lie structures on Borel subalgebras of finite-dimensional simple Lie algebras
• Mathematics
• 2020
Abstract A Hom-structure on a Lie algebra is a linear map which satisfies the Hom-Jacobi identity for all A Hom-structure is called regular if is also a Lie algebra isomorphism. Let be a Borel
Matching Hom-Rota-Baxter algebras, matching Hom-dendriform algebras and matching Hom-pre-Lie algebras
• Mathematics
• 2020
In this paper, we introduce the Hom-algebra setting of the notions of matching Rota-Baxter algebras, matching (tri)dendriform algebras and matching (pre)Lie algebras. Moreover, we study the
Classification of 3-dimensional Hom-Lie algebras
• Mathematics
Journal of Physics: Conference Series
• 2019
We derive conditions for an arbitrary n-dimensional algebra to be a Hom-Lie algebra, in the form of a system of polynomial equations, containing both structure constants of the skew-symmetric
A commutative algebra approach to multiplicative Hom-Lie algebras
• Mathematics
Linear and Multilinear Algebra
• 2022
We use a method of commutative algebra to describe the affine variety \$\textrm{HLie}_{m}(\mathfrak{gl}_{n}(\mathbb{C}))\$ of all multiplicative Hom-Lie algebras on the general linear Lie algebra

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• Mathematics
• 2006
A Hom-algebra structure is a multiplication on a vector space where the structure is twisted by a homomorphism. The structure of Hom-Lie algebra was introduced by Hartwig, Larsson and Silvestrov and
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It is demonstrated how a simple linear-algebraic technique used earlier to compute the low-degree cohomology of current Lie algebras, can be utilized to compute other kinds of structures on such Lie
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The aim of this paper is to give a survey of nonassociative Hom-algebra and Hom-superalgebra structures. The main feature of these algebras is that the identities defining the structures are twisted
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Introduction Notational conventions 1. Basic definitions 2. The invariant bilinear form and the generalized casimir operator 3. Integrable representations of Kac-Moody algebras and the weyl group 4.
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• 2017
A Hom-structure on a Lie algebra (𝔤, [, ]) is a linear map σ : 𝔤 → 𝔤 satisfying the Hom–Jacobi identity: [σ(x), [y,z]] + [σ(y), [z,x]] + [σ(z), [x,y]] = 0 for all x,y,z ∈ 𝔤. A Hom-structure is
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• 2015
Abstract A Hom-structure on a Lie algebra (g,[,]) is a linear map σ W g σ g which satisfies the Hom-Jacobi identity: [σ(x), [y,z]] + [σ(y), [z,x]] + [σ(z),[x,y]] = 0 for all x; y; z ∈ g. A