MULTIPLIERS OF THE TERMS IN THE LOWER CENTRAL SERIES OF THE LIE ALGEBRA OF STRICTLY UPPER TRIANGULAR MATRICES

Abstract

A Lie algebra multiplier parallels the idea of group theory’s Schur multiplier. This paper classifies the Lie algebra multipliers for all Lie algebras in the lower central series of strictly upper triangular matrices. Multipliers are central, so the classification is focused on computing their dimensions. The calculations are lengthy because balancing various matrix positions plays an important role in determining these dimensions. The result divides into six cases and the dimensions are given as polynomials in the size of the matrices and the position in the lower central series.

Keywords

• multiplier, Lie algebra multiplier, Schur multiplier