Moduli of Einstein and Non-Einstein Nilradicals

The subject of left-invariant Ricci soliton metrics on nilpotent Lie groups has enjoyed quite a bit of attention in the past several years. These metrics are intimately related to left-invariant Einstein metrics on non-unimodular solvable Lie groups. In fact, a classification of one is equivalent to a classification of the other. In this note, we focus our attention on nilpotent Lie groups and Lie algebras. We refer the reader to [Heb98, Lau07], and references therein, for more information about the connection between solvable and nilpotent groups with said metrics. If a nilpotent Lie group admits a left-invariant Ricci soliton metric, then it is called an Einstein nilradical ; otherwise it is called a non-Einstein nilradical. In this note we are concerned with the following question.