The log-Cherlin–Zilber conjecture for absolutely simple Lie rings

Let $T$ be a finite-dimensional theory, meaning that it carries a dimension function on interpretable sets satisfying the usual invariance, finiteness, union, and fiber-dimension axioms. Let $\mathfrak{g}$ be an absolutely simple definable Lie ring of finite dimension in such a theory and of sufficiently large characteristic. Log-Cherlin–Zilber conjecture. There is a definable Lie subring $\mathfrak{h}$ of finite index in $\mathfrak{g}$ and a finite Lie subring $\mathfrak{h}_0$ such that $\mathfrak{h}/\mathfrak{h}_0$ is a Lie algebra of finite dimension over a definable perfect field $K$. This is proposed as a generalization of the corresponding conjecture for Lie rings of finite Morley rank; the supplied text does not state whether it has been proved or remains open.