Leibniz algebras constructed by representations of General Diamond Lie algebras

2016/05/27 by Camacho, L. M., Karimjanov, I. A., Ladra, M. +1
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1605.08796

Abstract

In this paper we construct a minimal faithful representation of the (2m+2)-dimensional complex general Diamond Lie algebra, \mathfrakD_m(ℂ), which is isomorphic to a subalgebra of the special linear Lie algebra \mathfraksl(m+2,ℂ). We also construct a faithful representation of the general Diamond Lie algebra \mathfrakD_m which is isomorphic to a subalgebra of the special symplectic Lie algebra \mathfraksp(2m+2,ℝ). Furthermore, we describe Leibniz algebras with corresponding (2m+2)-dimensional general Diamond Lie algebra \mathfrakD_m and ideal generated by the squares of elements giving rise to a faithful representation of \mathfrakD_m.

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