Minimal representations for 6-dimensional nilpotent Lie algebra

Abstract

Given a Lie algebra , let μ(g) and μnil(g) be the minimal dimension of a faithful representation and nilrepresentation of , respectively. In this paper, we give μ(g) and μnil(g) for each nilpotent Lie algebra of dimension 6 over a field of characteristic zero. We also give a minimal faithful representation and nilrepresentation in each case.