Metric Lie algebras with maximal isotropic centre

TL;DR

This paper develops a classification scheme for a specific class of solvable metric Lie algebras, focusing on those with maximal isotropic centre and index 2, using a new theory of twofold extensions.

Contribution

It introduces a novel theory of twofold extensions for orthogonal representations, enabling classification of certain indecomposable metric Lie algebras.

Findings

Classified indecomposable metric Lie algebras with maximal isotropic centre

Provided a classification of metric Lie algebras of index 2

Developed a new theoretical framework for twofold extensions

Abstract

We investigate a certain class of solvable metric Lie algebras. For this purpose a theory of twofold extensions associated to an orthogonal representation of an abelian Lie algebra is developed. Among other things, we obtain a classification scheme for indecomposable metric Lie algebras with maximal isotropic centre and the classification of metric Lie algebras of index 2.