15 problems

Let $\mathfrak{g}$ be an infinite simple Lie ring of finite Morley rank, and suppose that its characteristic is sufficiently large. Cherlin–Zilber conjecture for Lie rings. Then…

A definable simple Lie ring of finite Morley rank is a Lie ring $\mathfrak{g}$ definable in a structure of finite Morley rank. Its characteristic is the characteristic associated w…

Let $\mathcal{L}$ be a nilpotent Lie lattice considered in CSV/19, let $K$ be a number field, and for each decomposition type $(\mathbf{e},\mathbf{f})$ let…

Let $\mathfrak{f}_{c,d}$ denote the free class-$c$ nilpotent Lie rings on $d$ generators defined over $\mathbb{Z}$. For $c,d\in\mathbb{N}$, let…

Medvedev's conjecture. $L$ contains a solvable subring of $m$-bounded derived length whose index is $(p,n,m)$-bounded.

A Lie algebra is semisimple if it has no nonzero solvable ideals, and an iUA-Lie ring is a Lie ring for which every commutator-preserving injection into another Lie ring is additiv…

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 a…

Let $\mathfrak{g}$ be an infinite simple Lie ring of finite Morley rank. Assume that its characteristic is sufficiently large. Large-characteristic conjecture. Then $\mathfrak{g}$…

Simple Lie rings of finite Morley rank are the model-theoretic analogue of the objects classified by the Block–Premet–Strade–Wilson theorem. Classification conjecture. Classifying…

Let $p\geq 2$ be prime, let $m=p$ be odd, and consider the Lie ring of partitions in which each part occurs at most $m-1$ times, with its recursively defined idealizer chain. Let…

Let $m\geq 2$ and consider the Lie ring of partitions in which each part occurs at most $m-1$ times, together with its recursively defined idealizer chain starting from the abelian…

For each $c\in\mathbb{N}$, let $\mathfrak{f}_{c,2}$ be the free class-$c$ nilpotent Lie ring on two generators, and let…

Let $\mathfrak{f}_{c,d}$ be the free class-$c$ nilpotent Lie ring on $d$ generators, and let $\zeta_{\mathfrak{f}_{c,d}}^{\triangleleft}(s)$ denote its ideal zeta function. du Saut…

Let $\mathcal{L}$ be a nilpotent Lie lattice considered in CSV/19, let $K$ be a number field with ring of integers $\mathcal{O}_K$, and let $(\mathbf{e},\mathbf{f})$ be a decomposi…

Let $\mathcal{L}$ be a graded Lie lattice. A grading is a decomposition of the underlying free $\mathbb{Z}$-module compatible with the Lie bracket, and its weight is the correspond…