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19952026
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23 papers · 1 filter

math.RA2024

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…

math.RA2022★ 2 cited

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…

math.RA2022

Lie structures and chain ideal lattices

Pilar Benito, Jorge Roldán-López

The purpose of this paper is twofold. Firstly, to emphasise that the class of Lie algebras with chain lattices of ideals are elementary blocks in the embedding or decomposition of…

math.RA2022★ 1 cited

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…

math.RA2022★ 2 cited

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…

math.RA2020★ 3 cited

Fine gradings on Kantor systems of Hurwitz type

Diego Aranda-Orna, Alejandra S. Córdova-Martínez

We give a classification up to equivalence of the fine group gradings by abelian groups on the Kantor pairs and triple systems associated to Hurwitz algebras (i.e., unital composit…