Solvable Lie algebras with Borel nilradicals (Q2879926)

In this work, the authors focus on analyzing the structural properties of real solvable Lie algebras, the nilradicals of which correspond to the nilradical of Borel subalgebras of complex simple Lie algebras and their normal real form. Albeit the nilradicals of Borel subalgebras and Borel subalgebras themselves have been analyzed in detail in the literature, no systematic study of their solvable extensions had been developed. The solvable extensions are studied according to their rank, among other characterizing properties, and it is shown in a new way that the maximal extension by non-nilpotent elements corresponds to the Borel subalgebra of the given simple Lie algebra. The solvable algebras obtained in this paper contribute to a better understanding of the class of solvable real Lie algebras, as the nilradicals correspond to nilpotent Lie algebras of different types, and the results are potentially of interest in the theory of integrable systems.