On maximal extensions of nilpotent Lie algebras

TL;DR

This paper investigates the maximal extensions of finite-dimensional nilpotent Lie algebras, demonstrating that such extensions are generally not unique, thereby challenging previous assumptions in the field.

Contribution

It proves that maximal extensions of nilpotent Lie algebras are not unique, refuting a prior assumption by L. Snoble.

Findings

Maximal extensions of nilpotent Lie algebras are generally non-unique.

The result refutes L. Snoble's assumption of uniqueness.

Provides new insights into the structure of nilpotent Lie algebra extensions.

Abstract

The maximum extensions of finite-dimensional nilpotent Lie algebras are considered. In particular, it is proved that in the general case such an extension is not unique, which refutes one L. Snoble's assumption.