Schur Multipliers of Nilpotent Lie Algebras

TL;DR

This paper investigates the Schur multipliers of finite dimensional nilpotent Lie algebras, establishing bounds on their dimensions based on algebraic properties, and compares these bounds with existing results.

Contribution

It provides a direct proof of an upper bound for the Schur multiplier's dimension in relation to the algebra's class and generators, enhancing understanding of their structure.

Findings

Schur multiplier is non-zero for dimensions greater than one.

Derived an explicit upper bound for the multiplier's dimension.

Compared new bound with previously known bounds.

Abstract

We consider the Schur multipliers of finite dimensional nilpotent Lie algebras. If the algebra has dimension greater than one, then the Schur multiplier is non-zero. We give a direct proof of an upper bound for the dimension of the Schur multiplier as a function of class and the minimum number of generators of the algebra. We then compare this bound with another known bound.