## 14 Citations

When Hom-Lie structures form a Jordan algebra

- MathematicsJournal of Algebra and Its Applications
- 2022

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

- 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

- MathematicsInt. 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

- MathematicsLinear 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…

## References

SHOWING 1-10 OF 19 REFERENCES

Low-dimensional cohomology of current Lie algebras and analogs of the Riemann tensor for loop manifolds

- Mathematics
- 2005

On Hom-algebra structures

- 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…

A Compendium of Lie Structures on Tensor Products

- Mathematics
- 2014

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…

Paradigm of Nonassociative Hom-algebras and Hom-superalgebras

- Mathematics
- 2010

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…

Infinite Dimensional Lie Algebras

- Mathematics
- 1983

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.…

Hom-structures on simple graded Lie algebras of finite growth

- Mathematics
- 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…

Hom-structures on semi-simple Lie algebras

- Mathematics
- 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…