Hom-Lie algebra structures on semi-simple Lie algebras
By Quanqin Jin, Xiaochao Li. 2008
105 citations recorded by the source corpus.
Abstract Hom-Lie algebras can be considered as a deformation of Lie algebras. In this note, we prove that the hom-Lie algebra structures on finite-dimensional simple Lie algebras are trivial. We find when a finite-dimensional semi-simple Lie algebra admits non-trivial hom-Lie algebra structures and the isomorphic classes of non-trivial hom-Lie algebras are determined.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/8ed53138c0ef1f67439d3b9e7a3728fcbfdee336
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In Algebra and Number Theory
- Abdenacer Makhlouf
- Donald Yau
- S. Benayadi
- Sergei Silvestrov
- F. Ammar
- Y. Sheng
- Aron Gohr
- Florin Panaite
In Discrete Mathematics and Combinatorics
In Geometry and Topology
- Abdenacer Makhlouf
- Donald Yau
- S. Benayadi
- F. Ammar
- Florin Panaite
- Sergei Silvestrov
- Aron Gohr
- Y. Sheng
Citations in the corpus
- Rota–Baxter Hom-Lie–Admissible Algebras (2011, background): “Further development could be found in, for example, [34, 56, 57, 7, 9, 56, 15, 46],[68]-[73], and the references therein.”
- Hom-bialgebras and comodule Hom-algebras (2008, unknown): “Other papers concerning Hom-type structures are [2]- [7], [10], [17] - [21], and [24] - [27].”
- Hom-Lie Algebras with Symmetric Invariant NonDegenerate Bilinear Forms (2010, background): “In [23], the authors studied when a finite-dimensional semi-simple Lie algebra admits non-trivial hom-Lie algebra structures.”