Hom-Lie algebra structures on quadratic Lie algebras and twisted invariant Killing-like forms defined on them

2020/10/12 by R. García-Delgado, García-Delgado, R., G. Salgado +3
Mathematics · #17B30 #17B40 #17B60. Secondary: 17B20 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary:17Bxx #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2010.06057

openalex publication_date 2020/10/12 · openalex created_date 2020/10/22 · openalex updated_date 2026/07/28

Abstract

Hom-Lie algebras defined on central extensions of a given quadratic Lie algebra that in turn admit an invariant metric, are studied. It is shown how some of these algebras are naturally equipped with other symmetric, bilinear forms that satisfy an invariant condition for their twisted multiplication maps. The twisted invariant bilinear forms so obtained resemble the Cartan-Killing forms defined on ordinary Lie algebras. This fact allows one to reproduce on the Hom-Lie algebras hereby studied, some results that are classically associated to the ordinary Cartan-Killing form.

Related

• Hom-Lie Algebras with Symmetric Invariant NonDegenerate Bilinear Forms
• On quadratic Hom-Lie algebras with twist maps in their centroids and their relationship with quadratic Lie algebras
• Inductive description of quadratic Hom-Lie algebras with twist maps in the centroid
• Invariant metrics on central extensions of Quadratic Lie algebras
• On Hom-algebra structures