Minimal representations for 6-dimensional nilpotent Lie algebra

Abstract

Given a Lie algebra [Formula: see text], let [Formula: see text] and [Formula: see text] be the minimal dimension of a faithful representation and nilrepresentation of [Formula: see text], respectively. In this paper, we give [Formula: see text] and [Formula: see text] for each nilpotent Lie algebra [Formula: see text] of dimension [Formula: see text] over a field [Formula: see text] of characteristic zero. We also give a minimal faithful representation and nilrepresentation in each case.