The nilpotent Lie algebra toral rank conjecture

Let $L$ be a finite-dimensional nilpotent Lie algebra defined over the rational numbers, and let $C(L)$ denote its center. Nilpotent Lie algebra toral rank conjecture. Then

$$\dim H^*(L;{\mathbb{Q}})\geq 2^{\dim C(L)}.$$

This is the reformulation of the toral rank conjecture for nilmanifolds in terms of Lie algebra cohomology, using the identification of rational toral rank with the dimension of the center. The paper constructs counterexamples in the nilpotent setting, so the conjecture is refuted.