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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References

SHOWING 1-10 OF 19 REFERENCES
Hom-Lie algebra structures on semi-simple Lie algebras
On Hom-algebra structures
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
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
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
Deformations of Lie Algebras using σ-Derivations
Infinite Dimensional Lie Algebras
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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