6 problems

Let $\mathfrak g$ be a finite-dimensional Lie algebra, let $n$ be a positive integer, and let $x_1,\ldots,x_n\in\mathfrak g$. Define … For each $i$, let $\partial_{x_i}F_i$ be the…

Let $k$ be the coefficient field, let $\mathfrak{fr}k(x0,x1)$ be the completed free Lie algebra on $x0,x1$, and let $\psi{451}$, $\psi{123}$, and $l^{y,x}{(a1,\dots,am),(b1,\dots,bn)}$…

Let $\widehat{\mathfrak{lkv}}_2$ be the linearized Kashiwara–Vergne Lie algebra, bigraded by weight and depth. Let $\mathrm{BK}_{W,D}$ be the coefficients defined by … with $s,t$ f…

Let the four Lie algebras in the inclusions referred to in the source be graded by weight, and let the associated graded Lie algebras for the depth filtration be included as in the…

Motivic Grothendieck–Teichmüller criterion. The inclusion

For each integer $k\geq 1$, let $\widehat{\mathfrak{krv}}^{(k)}_2$ and $\widehat{\mathfrak{krv}}^{(k+1)}_2$ denote the successive filtered Kashiwara–Vergne Lie algebras. Stabilizat…