8 papers
On quadratic Lie algebras containing the Heisenberg Lie algebra
R. García-Delgado
In this work we study quadratic Lie algebras that contain the Heisenberg Lie algebra $\h_m$ as an ideal. We give a procedure for constructing these kind of quadratic Lie algebras a…
Homogeneous quadratic Lie super algebras
R. García-Delgado
In this work we state a version of the double extension for homogeneous quadratic Lie super algebras that includes even and odd cases. We prove that any indecomposable, non-simple…
Invariant Metrics on Nilpotent Lie algebras
R. García-Delgado
We state criteria for a nilpotent Lie algebra $\g$ to admit an invariant metric. We use that $\g$ possesses two canonical abelian ideals $\ide(\g) \subset \mathfrak{J}(\g)$ to deco…
Inductive description of quadratic Hom-Lie algebras with twist maps in the centroid
R. García-Delgado
In this work we give an inductive way to construct quadratic Hom-Lie algebras with twist maps in the centroid. We focus on those Hom-Lie algebras which are not Lie algebras. We pro…
On Cohomology group of current Lie algebras
R. García-Delgado
In this work we state a result that relates the cohomology groups of a Lie algebra and a current Lie algebra , by means of a short…
Double extensions for quadratic Hom-Lie algebras with equivariant twist maps
R. García-Delgado, G. Salgado, O. A. Sánchez-Valenzuela
Quadratic Hom-Lie algebras with equivariant twist maps are studied. They are completely characterized in terms of a maximal proper ideal that contains the kernel of the twist map a…
On quadratic Hom-Lie algebras with twist maps in their centroids and their relationship with quadratic Lie algebras
R. García-Delgado, G. Salgado, O. A. Sánchez-Valenzuela
Hom-Lie algebras having non-invertible twist maps in their centroids are studied. Central extensions of Hom-Lie algebras having these properties are obtained and shown how the same…
Covariant functors commuting with direct limits
R. García-Delgado
In this work we state conditions on a covariant right exact functor so that it commutes with direct limits. These conditions are related to the commutativity of the functor under d…