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}
}
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78 Citations
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78 Citations

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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…
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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…
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References

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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.-…
Deformations of Lie Algebras using σ-Derivations
Infinite dimensional Lie algebras: Frontmatter
Infinite Dimensional Lie Algebras, third ed
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