# 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} }

Abstract We describe Hom-Lie structures on affine Kac–Moody and related Lie algebras, and discuss the question when they form a Jordan algebra.

## 13 Citations

Hom-Lie structures on 3-dimensional skew symmetric algebras

- Mathematics
- 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

- Mathematics
- 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

- Mathematics, Computer ScienceInt. 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

- MathematicsJournal 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
- 2019

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…

Generalized derivations and Hom-Lie algebra structures on

- MathematicsCommunications in Algebra
- 2021

The purpose of this paper is to show that there are Hom-Lie algebra structures on $\mathfrak{sl}_2(\mathbb{F}) \oplus \mathbb{F}D$, where $D$ is a special type of generalized derivation of…

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