Multipliers for the Lower Central Series of Strictly Upper Triangular Matrices

Abstract

Lie algebra multipliers and their properties is a recent area of study. A multiplier is the Lie algebra analogue of the Schur multiplier from group theory. By definition a multiplier is central, so we only need to find its dimension in order to characterize it. We will investigate how to find the dimensions of the multipliers for the lower central series of strictly upper triangular matrices. The closed form result is a set of six polynomial answers in two variables: the size of the matrix and the position in the series.