Hom-Lie Algebras with Symmetric Invariant NonDegenerate Bilinear Forms
By S. Benayadi, Abdenacer Makhlouf. 2010
197 citations recorded by the source corpus.
The aim of this paper is to introduce and study quadratic Hom-Lie algebras, which are Hom-Lie algebras with symmetric invariant nondegenerate bilinear forms. We provide several constructions leading to examples and extend the double extension theory to Hom-Lie algebras. We reduce the case where the twist map is invertible to the study of involutive quadratic Lie algebras. We establish a correspondence between the class of involutive quadratic Hom-Lie algebras and quadratic simple Lie algebras with symmetric involution. Centerless involutive quadratic Hom-Lie algebras are characterized. Also elements of a representation theory for Hom-Lie algebras, including adjoint and coadjoint representations are supplied with application to quadratic Hom-Lie algebras.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/e383510ed169519f5ffe1884c3e89ab909a22ae0
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In Algebra and Number Theory
- Florin Panaite
- Y. Sheng
- G. Graziani
- Claudia Menini
- Abdenacer Makhlouf
- Donald Yau
- Sergei Silvestrov
- F. Ammar
In Geometry and Topology
- Florin Panaite
- Y. Sheng
- Abdenacer Makhlouf
- G. Graziani
- Claudia Menini
- Donald Yau
- Michael E. Hoffman
- F. Ammar
In Mathematical Physics
Citations in the corpus
- Representations of Hom-Lie Algebras (2010, background): “ algebras have the structure of a hom-Lie algebra [5]. Because of close relation to discrete and deformed vector fields and differential calculus [5, 7, 8], hom-Lie algebras are widely studied recently [1, 2, 9, 10, 12, 13, 14]. In nowadays mathematics, much of the research on certain algebraic object”
- BiHom-associative algebras, BiHom-Lie algebras and BiHom-bialgebras (2015, background): “In the last years, many concepts and properties from classical algebraic theories have been extended to the framework of Hom-structures, see for instance [2, 3, 7, 8, 11, 16, 20, 22, 25, 26, 27, 31, 30].”