Applying Matrix Theory to Classify Real Solvable Lie Algebras Having 2-Dimensional Derived Ideals

Abstract

We present a new approach to the problem of classifying real solvable Lie algebras having 2-dimensional derived ideals. Partial results on this problems were obtained by Schöbel in 1993 and by Janisse in 2010. We add some new infinite families of Lie algebras to these classifications. Moreover, in association with the results by Eberlein in 2003, we achieve a complete classification for real solvable Lie algebras having 2-dimensional derived ideals.