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}
}
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14 Citations
Background Citations
3
Methods Citations
2

14 Citations

Citation Type

Citation Type

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
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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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
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
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
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…
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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
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
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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References

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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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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
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
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…
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