2 citations · 5 across the 7 of their papers we have counts for
7 papers
Computing Derivations on Nilpotent Quadratic Lie Algebras
Pilar Benito, Javier Rández-Ibáñez, Jorge Roldán-López
Every non-solvable and non-semisimple quadratic Lie algebra can be obtained as a double extension of a solvable quadratic Lie algebra. Thanks to a partial classification of nilpote…
Skew-adjoint maps and quadratic Lie algebras
Pilar Benito, Javier Rández-Ibáñez, Jorge Roldán-López
The procedure of double extension of vector spaces endowed with non-degenerate bilinear forms allows us to introduce the class of generalized $\mbK$-oscillator algebras over any ar…
Metrics related to Oscillator algebras
Pilar Benito, Jorge Roldán-López
A Lie algebra is said to be metric if it admits a symmetric invariant and nondegenerate bilinear form. The harmonic oscillator algebra, which arises in the quantum mechanical descr…
Examples and patterns on quadratic Lie algebras
Pilar Benito, Jorge Roldán-López
A Lie algebra is said to be quadratic if it admits a symmetric invariant and non-degenerated bilinear form. Semisimple algebras with the Killing form are examples of these algebras…
Equivalent constructions of nilpotent quadratic Lie algebras
Pilar Benito, Jorge Roldán-López
The double extension and the T*-extension are classical methods for constructing finite dimensional quadratic Lie algebras. The first one gives an inductive classification in chara…
Derivations and automorphisms of free nilpotent Lie algebras and their quotiens
Pilar Benito, Jorge Roldán-López
Let $\n_{d,t}$ be the free nilpotent Lie algebra of type and nilindex . Starting out with the derivation algebra and the automorphism group of $\n_{d,t}$, we get a natural d…
Lie Algebras with a finite number of ideals
Pilar Benito, Jorge Roldán-López
In this paper we focus on the structure of the variety of Lie algebras with a finite number of ideals and their graph representations using Hasse diagrams. The large number of nece…