Hom-Lie algebra structures on semi-simple Lie algebras

@article{Jin2008HomLieAS,
  title={Hom-Lie algebra structures on semi-simple Lie algebras},
  author={Quanqin Jin and Xiaochao Li},
  journal={Journal of Algebra},
  year={2008},
  volume={319},
  pages={1398-1408}
}
Hom-Lie superalgebra structures on finite-dimensional simple Lie superalgebras
Hom-Lie superalgebras, which can be considered as a deformation of Lie superalgebras, are $\mathbb{Z}_2$-graded generalization of Hom-Lie algebras. In this paper, we prove that there is only the
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
Generalized derivations and Hom-Lie algebra structures on
Abstract The purpose of this paper is to show that there are Hom-Lie algebra structures on where D is a special type of generalized derivation of and is an algebraically closed field of
On Hom–Lie algebras
In this paper, first we show that is a Hom–Lie algebra if and only if is an differential graded-commutative algebra. Then, we revisit representations of Hom–Lie algebras and show that there are a
HOM-LIE ALGEBRAS ON STRICTLY UPPER TRIANGULAR MATRICES LIE ALGEBRA OVER A COMMUTATIVE RING: DERIVATION CASE
Let n be the nilpotent Lie algebra consisting of all strictly upper triangular n n × matrices over a commutative ring. In this paper, we characterize the decomposition of the derivations of n when (
Hom-structures on finite-dimensional simple Lie superalgebras
A Hom-structure on a Lie superalgebra is an even linear mapping which twists the super Jacobi identity. In this paper, using Kac’s classification theorem and a reduction method, we show that
Current Hom-Lie algebras
In this paper, we study Hom-Lie structures on tensor products. In particular, we consider current Hom-Lie algebras and discuss their representations. We determine faithful representations of minimal
Purely Hom-Lie bialgebras
In this paper, we first show that there is a Hom-Lie algebra structure on the set of (σ, σ)-derivations of an associative algebra. Then we construct the dual representation of a representation of a
Global and Arithmetic Hom-Lie Algebras
Hom-Lie algebras are non-associative, non-commutative algebras generalizing Lie algebras by twisting the Jacobi identity by a homomorphism. The main examples are algebras of twisted derivations
...
...

References

SHOWING 1-4 OF 4 REFERENCES
Introduction to Lie Algebras and Representation Theory
Preface.- Basic Concepts.- Semisimple Lie Algebras.- Root Systems.- Isomorphism and Conjugacy Theorems.- Existence Theorem.- Representation Theory.- Chevalley Algebras and Groups.- References.-
Infinite Dimensional Lie Algebras, third ed
  • 1990